If a player rolled a ball to me across the dugout indeed yes, I would probably keep it.

My two best "ball" stories.
Was at a Japanese minor league game and thought it would be cool to have a ball from a Japanese game but no foul balls were forthcoming. Went down to the bathroom, which was on lower concourse with open door, and heard a bouncing sound behind and foul ball rolled into bathroom. I kid you not.

Second is just as strange. As a kid used to go to Portland Beaver games and found a vendors hat so put hat on and walked down stairs to bowels of stadium and access to field. Sat in bullpen with pitchers and collected two home run balls. Rick Jones, former MLB pitcher and then -Bevo turned to me and said, "Aren't you supposed to be working?" Gag worked for seven games until I was chased away by vending supervisor.