I don’t think so. He was against Harry in private, as well.
He didn’t REALLY try to teach him Occlumency, and he was constantly putting him down to Dumbledore, too.
The occlumency thing is funky, on the one hand Snape was pretty quick to give up teaching Harry, but on the other side Harry a definite “screw you I won’t learn from you” attitude. I think Snape tried but Harry gave him so much resistance, then went poking around in Snape’s head and that was pretty much it. As for his putting down Harry in front of Dumbledore I think that ties to the whole discipline and James thing, Dumbledore was fond of letting Harry do whatever, kind of like how James got to do whatever. I think Snape wanted the James beaten out of Harry so he could be more his mother’s son.
But inclined as I am to feel bad for Snape - he choose his bed. His actions drove Lily away. If he had done as Lily asked there might have been a sliver of a chance. Then to barter the lives of a baby and James for Lily - that's awful.