No but as you say they tested the basic idea with the "Putt-Putt" (the nickname for Orion being "Bang Bang").
I found a video of "Putt-Putt" in action.
I did say that. What they were testing was the question of whether a craft propelled by successive explosions would be controllable or not, not developing an efficient rocket system.
Here is an article on the concept of energy density, including a table listing it for many substances. TNT has energy density of 4.6 MJ/kg; kerosene is ten times that, 46 MJ/kg.
Now then imagine a spacecraft propelled by successive TNT explosions. Say we have the 5 ton capsule I suggested might be adequate, and it has a 1 ton gun on a spring attached to it. The gun has an ingenious mechanism that automatically loads in another explosive charge of TNT (with detonator built in) into the breech of the gun, that has a door that is opened for loading when the gun recoils against the spring, takes the next charge, closes and locks the breech, and detonates the charge when the spring has expanded to zero stress extension. Compressing the spring to full with this size charge takes 1/2 second. The charges thus explode once per second, and propel the whole six ton arrangement at 10 meters/sec^2 average acceleration. To push 6000 kg at that rate, each charge must deliver 60,000 Newton-seconds of impulse.
At 4.6 MJ per kg, from kinetic energy = 1/2 mass*velocity squared, we can see that detonating 1 Kg of the stuff releases enough energy to propel its own mass to 3033.15 m/sec. Thus a 20 kilogram charge is the right size to get the needed recoil on the gun.
This does not admittedly look so bad. With the charge blasting out of the gun at 3 km sec, we appear to have an ISP of 309 seconds!
Well now look at kerosene, credited with ten times the energy "stored" in it. Actually if we read the description of the table, this means how much energy would be released if were burned with the necessary mass of oxygen to combust it all, and does not count that mass. If a unit of a hydrocarbon has about 2 hydrogen atoms and one carbon, its molecular weight is 14, while it would need 3 oxygen atoms massing 16 AMU each. Note that realistic rocket engines rarely burn at the perfect stoichiometric ratio, preferring to be a bit fuel rich. Let's suppose we use 9/10 the stoichiometric ratio of oxygen, for 9/10 the energy release, we now have 41.4 MJ for 4.086 kg of material, or only 10.132 MJ/kg. That still amounts to a velocity of 4502 meters/sec. Ideally. But a realistic kerosene-oxygen rocket does very well indeed to get a nozzle exit velocity as high as 3500 m/sec. But that is still better than 3 km/sec!
This suggests that there may be serious problems I had not allowed for in the TNT gun rocket idea, aside from all the mechanical issues involved with guaranteeing the loading/latching/firing mechanism works. Perhaps for instance a realistic gun barrel will not capture a big fraction of the theoretical exhaust energy available; it would take an infinite nozzle to convert all the thermal energy theoretically available to collimated kinetic energy directed back on the axis. Our intuition tells us even if the gun barrel is fairly long and shaped like an efficient nozzle, what comes out is a puff of very hot dense gas that has a lot of expansive energy left in it--that energy is not contributing to the impulse, which is therefore lower than 3 km/sec effectively. In fact we may be up against some fundamental thermodynamics--a big portion of the energy is entropic and not available to harnessed by any means perhaps. A realistic high efficiency kerosene-oxygen rocket is presumably losing a similar portion of its total energy. If in theory (disregarding thermodynamics) the exhaust could have been a mass at absolute zero temperature moving back at 4500 m/sec, but we really get a hot gas with net backward speed of 35, the speed ratio is 7/9 and in energy terms, that is squared, or 49/81, or just 60 percent of the total energy harnessed to useful thrust. If a similar ratio holds for the same fundamental reasons for the TNT blast drive, the real muzzle velocity of the gas bolus would be 2360 m/sec, and the necessary mass of the charge would be 25.42 kg instead; we'd use up a ton in less than 40 seconds, not 50. That is an Isp of over 240 sec to be sure! So not as good as a mediocre ker-lox rocket, but comparable to von Braun's alcohol-oxygen V-2 engine or all but the most efficient peroxide engines.
I suspect the real ISp, even in a very efficiently shaped gun, would be lower than 240, because high-efficiency ker-lox engines like Russian-made staged combustion engines (we never went for such high Isp in our ker-lox engines here in the States) are working very close to equilibrium, whereas explosions are an example of non-equilibrium processes that inherently produce higher entropy, which is a way of restating they are irreversible processes.
This TNT gun works in vacuum of course. For a realistic launching system, it needs to operate at much higher thrusts, against the atmosphere, which will stall the exhaust somewhat and rob it of more thrust. We need a bigger gun, able to take much bigger charges, and the right size and rate of charges for launching from the ground would be far greater than later phases where half or more of the total magazine of charges has been emptied already.
My computer is too rickety for me to risk running videos on it, but from what I know of Orion, the system demonstrated in the test is a model of the Orion concept, which is a lot less efficient than putting a charge in the breech of a good nozzle-shaped gun and firing it. They could have done an efficient gun for this test and that's probably what some ATl society trying to launch spacecraft on chemical explosions would do, but the idea was to model Orion, where the notion of making a gun to enclose a fission explosion was absurdly impossible; the curved reflector plate concept itself was almost inconceivable until empirical experiences at testing sites demonstrated that solid materials could be protected from being destroyed by nearby nuclear fireballs. Thus, the model shares an inherent inefficiency of Orion, which is that much of the blast will miss the plate completely and what does hit it is inefficiently bounced off at a less than perfectly efficient angle. This will also eat into the effective Isp of any design taking advantage of the simplicity of the plate rather than investing in a collimating gun.
I'd be willing to bet at this point that even a more efficient design than Jerry Pournelle had the desperate natives of Prince Samuel's World bung together would at any rate be far less efficient even than the poor propane pressure driven thing I suggested, not to mention that any mechanical failure spells doom for any crew, if they can indeed survive the battering that a succession of hard bangs will give them, springs or not. The magazine to hold enough explosive charges to put them into orbit will have a large empty mass, unless they stage several sized gun driven stages one after another--as they might have to, since designing for a given thrust is hard enough, but enabling a variable thrust is worse.
Be very steampunk neat if someone can prove me wrong though!