Yes! I don't think Sherlock had abusive parents. I think he was bullied, but then, a lot of smart kids are. He gets quite attached to John relatively quickly and clearly loves Mrs. Hudson, but most of all, he doesn't really seem surprised at their love for him. I read fics in which Sherlock is shocked that John cares about him, but what I see on the show is him taken aback when John corrects "friend" to "colleague." (I think John wanted to sound professional and not just like a hanger-on, and I don't think he realized that this bothered Sherlock.) I'd expect an abused Sherlock to be resigned to such treatment, not surprised that John didn't just accept "friend." Nor do I think he's really surprised that John tells him to run at the pool.

Sherlock also seems to treat Mrs. Hudson very much as a mother figure—and not to be surprised that she cares about him, chides him, fusses over him, whatever.