Yes my mum let my boyfriend visit and sleep over when I still stayed at home. She was ok with it from the moment we started going out although I think this was because we were friends beforehand so she knew him well. I think she'd have still been ok with me having my boyfriend stay over every now and then. She let us sleep in the same bed when he stayed over as I was 17 at that point.
As for his parents house, I was rarely allowed to visit and only stayed over when they were away at their caravan for a weekend every so often.