Yes but Snape has to see that Harry Potter is NOT James Potter. No matter how hard Snape tries, he will get no satisfaction from punishing Harry because Harry isn't the one who hurt him.

Moreover, once Snapes enemies find out what a sucker he is for punishing Harry, they will set him up. Snapes attitude is dangerous to himself as well as other members of the Order who depend upon him. It could be Snapes fatal flaw.