Thanks for all of the responses. It sounds like this is probably a bad idea, in part because I don't know anyone in FRA and don't really want to plan a layover. If it were someplace I didn't mind spending a day, I'd schedule a long layover.

I guess my one hope was that if I bought both tickets from united.com, united might help me in the case of a misconnect, but it sounds like it doesn't matter. Two PNRs are two PNRs, even if you buy them from the same place.