Nah. That doesn't fully indicate one way or another about the human quality of his mentality. The parasytes haven't yet done anything that would make them more monstrous than humans. It's such a cliche, but it's true. Shinichi probably won't easily be able to cry before he has dealt with the parasyte that stole his mother's body. It's quite a natural reaction, and no stranger than crying before doing anything about it, especially when he knows perfectly what's going on, unlike his old man. It also doesn't help that he earlier changed his opinion and blessed his parents' trips.