What is the largest amount of pebbles in mancala to win with?
First, the issues:

1: you've not defined which version. Yes, I know, yo've specified some starting conditions. But not the capture conditions.
2: There are literally hundreds of variants of Mancala, and at least 3 different capture mechanics I've played.
3: the normal setup is 12 pits... 6 per player...

Still, despite these, I think I can answer the question.

Given that I'm most familiar with Oh-wah-ree, the 3M bookcase game, which has a capture condition of "last stone played landed in an opponent's pit with 1, 2 or 3 stones already present, regress backward for additional pits captured"... And Oh-Wah-Ree's end is only one player can move, and can't provide a piece to another player (which is required if possible).

It is possible, in theory, to capture all the stones on the board in this variant.

In most variants, it's possible to capture all the stones, but not easy. 

In the variants where you sow to the capture pit at each end, it's virtually impossible as your opponent must sow at least the starting number of pebbles worth into their own capture (if your capture is at the end of your side) or you must sow theirs (if your capture is at the beginning of your side).