How to install a handheld shower without drilling the shower membrane?
The holes drilled for the mounting bracket of the handheld are extremely small and the bracket would further deflect water entry.

But to be especially safe, you can force a silicone sealant into the drilled holes before mounting the bracket. The screw will push it into the gap, and this will effectively heal the break in the waterproofing membrane.

If you are especially paranoid about moisture, put a dab of silicone sealant on the back of the mounting bracket itself.