Could Paul have been the replacement for Judas, had the disciples waited instead of casting lots (gambling)?
Yes, Paul COULD have been Judas' replacement. in fact, many Christian Scholars and Ministers (including myself) believe this.
The understanding is that Paul was God's choice for Judas' replacement, but the other guy, who was chosen by lots, was the human choice. But the choice was born due to human interference, while the other was promised by God...sort of like the issue between Isaac and Ishmael.
Although keep in mind that, though we'd recognize it today as gambling, casting lots was something commanded in the Law of Moses. Casting Lots was also often used for making decisions or distributing something between others (Here's a link to see some of these places). But it was always done in the presence of the Lord, which IS what the Apostles did for Judas' replacement.
I've personally always been skeptical about casting lots though. I mean, best 2 out of 3 means somebody in the group there will win, and shortest straw pulled will always end up in somebody's hand. Plus, throughout all of His ministry, Jesus continued to show His 12 that the ways of tradition were not to take the place of your worship for God, so I wonder if using this tradition could have also been recognized as a tradition that they should not have picked up for this matter, as you're suggesting.