If we're talking homomorphisms, no it can't: the whole point of the homomorphism is that the addition operation works regardless of whether you do it in the sou

If we're talking homomorphisms, no it can't: the whole point of the homomorphism is that the addition operation works regardless of whether you do it in the source space (2 + 4 = 6, then reduce mod 5) or the target space, where you're dealing with entirely different objects (2 mod 5 added to 4 mod 5, where each of these is an object in the target space and not an ordinary integer).