Do you think Aunt May will find out?

She doesn't know he's Spider-Man.

How would she know?
Sure he would have changed a little when he became Spider-Man and then gave it up. But she wouldn't jump to the conclusion that fast unless she had solid proof.

Aunt May knows NOTHING.

If she knew she wouldn't have thought Spider-Man was a bad guy originally.

And at what point in between her rescue from Ock and that little hero speech she made could she of found out Peter was Spider-Man seeing as he had quit being Spidey???