Velvett
Serious response.
There is no way to gage what kind of person she is since none of us know her. An offer of help is not too pushy in my opinion. It also covers things if she is really ill and something of the sensitive type. He at least demonstrated concern and consideration, even if she does not wish to see him. I can't see how that would hurt him. To the contrary, it demonstrates a regard beyong " I only wish to see you when I have a chance to get laid."
Conversely the only down side is coming across as liking her given the possibility that she doesn't reciprocate. So what. He won't die for having let some girl know he's interested only to find out she isn't That's a non issue in my opinion.