I know the deadline is in about a week, but Penn has been sending me promotional things all year, and just yesterday they sent me this nice big plastic packet with a letter addressed to me and lots of info. I know colleges send these out to everyone, but is there any chance that the school actually specifically wants me? Or do they just send it out generally?
They want you to apply; either they’ll get a new student or you’ll drive down their acceptance rate, which people use to judge the merits of some schools.
Your GPA and SAT may give you a shot, so if you’re interested, go for it. But don’t expect miracles from a school that rejects nine out of ten applicants, of course. 
They send it out generally. It’s all based on info from the collegeboard search. A school will send out these letters to any student who got above a certain score on their PSAT/SAT.
I got emails from Harvard and Stanford even though it’s obvious I would probably not get in if I had applied.
And you’ll notice (I do now), if you already got into a school or committed to one, you’ll still receive emails regardless