Is the mass of the electron neutrino the quantum of mass? Is the mass of the lightest neutrino, the electron neutrino, the quantum of mass? That is, is all mass in the universe an integer multiple of the mass of the electron neutrino?
 A: No. That would mean energy is quantized too. And energy can take any value.
The masses of the other elementary particles are no multiples of the mass of the neutrino, what would be the case if mass was quantified like you imagine. The neutrino ìs the lightest particle though. With a very small restmass. But mass doesn't come in units like charge.
A: Photons can be made with energy smaller, similar or larger than neutrino.
Neutrino has several types, two of them have similar mass with ratio below 2, and third is different, but we dont know yet how. If third type is heavier, then two lighter ones low mass ratio disproves your idea.
Black hole can be made heavier by a mass smaller than a neutrino. By throwing a photon in it, with an energy less than mass of a neutrino.
We dont have neutrino mass measured anywhere close to precision needed for your question if the third type of neutrino is significantly lighter than the other two.
So either we dont know or no. I would consider no to be more likely.
P.S. also neutrino oscillation likely throws a wrench in your idea as well, with their types changing, and probably their masses too
