Kinda. The magnetic field is the curl of the vector potential. If the vector potential is nonzero but curl-less then you get zero magnetic field, but the partic

Kinda. The magnetic field is the curl of the vector potential. If the vector potential is nonzero but curl-less then you get zero magnetic field, but the particles’ wavefunctions still feel the vector potential. (Specifically, the phase of the wavefunction is affected; obviously nothing observable about a single wavefunction could be affected in the absence of a field, via the correspondence principle. But when you have two electrons, that phase difference does show up in their interference pattern.)