All funerals are emotional but some ethnic groups tend to be a little more emotional than others and I think that Italian ones may be one of them. Because of that I don't think anyone will notice your tears and if they do they wont think anything of it.

Word of warning. If it is an open casket funeral don't go anywhere near the coffin. My aunt's funeral was and I was OK until I saw her lying there.... and then I lost it.