Should I even bother (Georgetown)?

Well, you do have the first gen hook, so there’s that. Your 1380 SAT is near the bottom 50% according to collegedata.com. And you need to include your unweighted GPA here for an accurate response. Given that your weighted are mostly <4.0, then your unweighted will be less.

EA increases chances somewhat, but I’m not sure it will be enough to overcome your score and unweighted GPA. If you aren’t wanting to apply anywhere else for EA, then I say write a killer essay and go for it.