Can I pump my MTB tire to max (55 psi / 380 kPa) without the tube inside bursting?
It can't burst the tube, because the tube is completely surrounded by the tyre and rim.

Bear in mind, though, that higher pressures don't automatically mean a faster ride. There are two competing factors: a soft tyre is constantly losing energy due to being squashed flat against the road, but a hard tyre loses energy because any bumps you go over have to lift the whole bike, instead of just deforming the tyre.  I don't ride mountain bikes so I don't know where that trade-off starts to bite.

On an e-bike, I'm not sure this will make much difference, though: it just means that the assist motor will have to work less hard at any given speed.