Angels were pretty much forbidden from relations with humans. Especially arch-angels, as they were supposed to be the ‘models’. Did this hold Gabriel back from endlessly perusing you? Absolutely not.

Gabriel had been staying with you all at the bunker, (Dean, Sam, Castiel, and Jack) much to certain annoyances. Gabriel was always flirting with you, despite how ‘forbidden’ it was. He didn't seem to care, even if the boys kept telling him how wrong it was. You were sitting at the library table, reading, while Gabriel sat right at your side, as always.