In interpretations of Quantum Mechanics that are Psi Ontic, in which the wave function is REAL ( Objective collapse theories, MWI, ect), does the wave function still physically spread to infinity? I know it does mathematically, but does it physically?
Lots of QM effects extend to infinity. Its a linear theory, which means that the solutions can extend indefinitely (and have to in order to keep the theory working). The probability density extent of one of the electrons your brain extends everywhere in the Universe. Its amplitude will be very small in most places to put it mildly, but without these huge areas of infinitesimal probability amplitude, the theory fails to have unitarity (i.e. probabilities adding to exactly 1) and fails.
My answer is for 'regular QM'. There is no difference between mathematically and physically in this case. If QM is correct (and lots of people think it is for some reason) then the wave function physically spreads to infinity.