A nova is generally understood as an explosion of a star. Thus comparing a nova to a stable neutron star is kind of a nonsensical thing to do.
If you're asking if a star goes nova and the core that remains is a neutron star after the resulting explosion, will it's mass increase overall? The answer is no, since it loses a lot of mass in the process of going nova. However, it is now more dense than before and the concentration of matter is in a much smaller space (the neutron star). (The explosion compresses part of the star and pushes the rest of it outward off into space).
If you're asking if a neutron star's mass will increase if you throw matter at it, the answer is yes. Just like any other form of matter. Is there a limit to how bit you can increase it? No; however, past a certain density it will compress into a black hole (which do not have a size limit as far as we know).
You may want to edit your question to clarify what you mean.