Honestly... no. It's POSSIBLE, but unlikely. Father Time comes for every athlete eventually, and when he does the effects are permanent. Ovechkin still is a top talent for now, but I don't know that he has enough time left at that peak to make up enough ground on the record.
Now, that said, if anyone COULD, he'd be my pick to get there. It's been a pleasure to be in DC for most of his career and see him firsthand. I've only seen someone who single-handedly changes a game the way be does once in my time watching the NHL- Peter Forsberg. I don't know how to give higher praise than that.
I'll say this- if he hadn't had his slump a few years ago during the Hunter/Oates years, where he looked merely good rather than superhuman, he might have had a better shot at this.