The Iraqis didn't have the rocket technology (of course, that's why they hired Bull!), which would probably have looked like the US "Sprint" missile, and at the very raw edge of what was feasible at the time.
Interestingly, though, you can get from the Moon back to the Earth using only a gun-type launcher, IIRC. Some lunar mining concepts use this as a way for mined minerals to get back home without uneconomical use of rocket fuel -- typical schemes I've seen tossed around use various electromagnetic launchers with solar panels or nuclear reactors providing the juice. I've never run the numbers myself -- maybe some Kerbal Space Program junkie can figure it out though?
Probably the best use case for gun-type launchers is for orbital transfers of unmanned cargo. There were some neat ideas tossed around in the 80s of having a big satellite or space station with a nuclear reactor serve as a launch platform for small cargo pods, which would lack their own engines. As long as you balanced the number of "up" and "down" pods, you could keep the launch platform in an approximately stable orbit, supposedly. Very hard to do without a big honking nuclear reactor though.
The critical problem with using a gun though, is the sheer amount of force applied when firing the gun. They couldn't even get dummy payloads to work correctly, the rockets motors warped due to the forces involved.
Although ridiculously difficult and inefficient, it's possible to achieve orbit with just a gun, and another body's gravitational field. It doesn't need to be captured by said field, it can just be influenced enough to stabilise it's orbit.
> In a three-body or larger system, a gravity assist trajectory might be available such that a carefully aimed escape velocity projectile would have its trajectory modified by the gravitational fields of other bodies in the system such that the projectile would eventually return to orbit the initial planet using only the launch delta-v [1]
[1]: https://en.wikipedia.org/wiki/Space_gun#Getting_to_orbit