Yep and it's a pretty easy thing to do.
There's prolly more than 1 way to do it, but what quickly comes to mind it's a matter of setting 3 different flags, each on each script where the player can choose his starter.
Then, whenever you want an event to happen if the Player chose a specific starter, you just:
checkflag 0xFlag
if 0x1 goto @EventsChain
And then just keep going, writing whatever actions you want to happen.
In your case, you're also gonna need to make 3 different trainerbattles and use them however you want.