Anything is possible of course, but Paul seems to have had a fairly high social standing. As a wealthy merchant with Roman citizenship, playing the mercenary would have gone against social conventions.

Wealthy Greeks and Romans of that era were snobs. Even serving in the legions as a ranker rather than a political officer (tribune) would have been a social liability.

Hiring oneself out for military jobs? Almost unthinkable. In an earlier era, the elite did things like that. But by Paul’s time, the elite hired people to do their military service. Or sometimes they sent slaves in their place.

Since we have no idea why Paul did what he did, one set of speculations is about as good as another. Setting out on a mission to kill proto-Christians would have been highly unlikely for any reason. So could he have done it for money? We have no way to know.