Thank you for bringing your question to Just Answer!
Unless he doesn't get out of work until Midnight, I think you are right to be concerned. It also seems odd that he wants you to convert while he's not willing to follow his church's guidelines for behavior. And by the way, people in bars talk on the phone all the time (and cell phones have vibrate options for loud places) so his excuse that he can't hear the phone doesn't hold water. There's a reason he's choosing to play pool so late at night, and I agree with the reason you gave for being worried--the attention from drunk women.
The very fact that you are engaged, he knows this behavior hurts you, and he chooses to continue doesn't bode well for a long term relationship. He may expect to
continue this after you are married. And when other things come up that you don't like, he may ignore your feelings then just like he is now.
This is not a man who is putting the happiness of his partner first. Don't convince yourself that marriage and children will change him. He's showing you who he is with this behavior. If you marry him, this is what your life will be like. Make sure you can handle that before committing to a man who doesn't think twice about hurting your feelings on a regular basis.