as revealed on Gil day 7 if you don't sit with Gil on the bus, Gil is still a virgin. so no, Gil and Edgar never slept with each other.
Gil strikes me as the type of person who wouldn't joke about that if it wasn't true. the way he immediately takes it back because he wants to be seen as a sex expert, and how he reacts when Lars teases him about it later seems consistent with that to me. i'm going to assume it's true until if/when it is proven otherwise. and even if the virgin thing is somehow a nonsensical red herring joke, i highly doubt he would've slept with Edgar because he was so determined to not be a homewrecker