Hmm. This question is trickier than it sounds. To know whether a body in a three-body system is always gravitationally "bound", you have to look into the future. For example, a close-enough flyby of the Moon on the trailing side would put the spacecraft on an Earth-Moon escape trajectory.
Apollo 11 was on a free return trajectory for which the lunar flyby (if it didn't go into orbit) would send it back to the Earth. So it was gravitationally bound, right?
Well, what if a spacecraft was on a very similar trajectory that just misses the Earth on the return. (I'm not going to use Apollo 11 in my hypothetical, since I don't want to kill the Apollo 11 astronauts, even hypothetically.) It would continue to orbit Earth in a lunar-crossing orbit, eventually having a close encounter with the Moon again. Then the Moon might fling the spacecraft on an escape trajectory. So was it gravitationally bound?
Exactly this happened to the Apollo 12 third stage you mentioned, which was orbiting the Earth for quite some time. It is believed to have left Earth orbit in 2003. Since it escaped three decades later, it must not have been gravitationally bound that whole time. But what if while in solar orbit it encounters the Earth-Moon system some time later, and the Moon does the opposite thing and puts it back in Earth orbit? (That third stage might do just that in the mid-2040's.) Now was it gravitationally bound the whole time? If now you think it is, might it not eventually escape again?
If its wanderings are permanently ended by impacting the Earth or the Moon, then it is now gravitationally bound in pieces on that body. So therefore it was always gravitationally bound, even when it was in solar orbit. Right?
To truly answer your question, you would need to propagate the trajectory from every state between maneuvers, potentially for a very long time, to determine its ultimate fate. There will often not be enough accuracy in the known state, as well as uncertainty in solar pressure perturbations, for that to even be deterministic.
As for that Apollo 12 third stage, they deliberately tried to have it immediately escape the Earth-Moon system, but failed. Later Apollo third stages were targeted to impact the Moon, which made for nice seismic signals.