I think about when Chase's dad died and how House reacted whenever he found out that Chase's dad was dying. I was very surprised. It was one of the first times that we saw that House did care about his ducklings.

hhhhhmmmmmm

He had his moments, but overall, no, I don't think so.

I always thought he kept Chase around mainly to dump on.

in some scenes he does show he cares about the ducklings.
the way he was fighting with chase after he killed that woman after chase's father died, the way he freaked when foreman was infected, how he went after cameron when she killed the old doctor....