"Applying" to schools after NSF GRFP?? - Mechanical Engineering

[MintTea.ME]

Hi all, perhaps you can help me out. I applied to four graduate schools for a PhD in mechanical engineering (two offers, one reject, and one waitlist) and until yesterday I thought I had my decision pretty much made (although I haven't accepted anything yet). However, now that I've been awarded an NSF GRF I'm confused: I've been told to approach my "dream schools" and a professor at Georgia Tech even reached out to me despite the fact that I didn't apply there.

Am I really able to email prestigious universities and ask them to admit me based on my NSF award? Also, doesn't that seem to be rushing things? I applied to my four schools because I have been talking with them for months...even before I sent in my applications.