My understanding is that yes, you can. You have to be scanned into the park to actually add Genie+ (unless it's already part of your ticket) but then afterwards you don't have to be in the park to make reservations.
If you've already scanned your ticket into your reserved park and have Genie+ for the day, you can make LL reservations for the rest of the day. We made reservations from the opposite park, our hotel, and DTD restaurants no problem.