To a degree, yes. As was mentioned elsewhere there is a thin called Wave Function Collapse, which occurs when a measurement is taken of a quantum system and forces the system into a state. A measurement could be seeing it, scanning it, bumping into it, etc (not human conscious observation, that’s an old and weird interpretation and not relevant nowadays).

Before (and after as well) you actually collapse the wave function you can perform meaningful math using the quantum particles. The one way I’m familiar with is for computer calculations, which is what quantum computers are aiming for. This is basically done by canceling out certain possibilities to only allow the wave function to collapse into ways that give meaningful mathematic results.

As such, this is barely relatable to a quantum Santa which uses this nature to perform meaningful present sharing actions simultaneously using quantum superposition of a quantum system that is spread out over a very large area. Of course, basic quantum mechanics becomes statistically the same as normal physics (i.e. 10 quadrillion particles average out to one normal human), so Santa would need to be a reality bender to allow for such small chances to occur to allow a human sized being to affect a huge area… but whatever.