Yes. Periods have never been an issue between me and my partner. While I don't really have much of a "flow" these days (medication I take for endometriosis stops it thank God!) I had extremely heavy ones when my partner and I first got together, and it never stopped us.
When I did have periods though, we would still have sex, just not when I was in pain. Thankfully, my lovie is not afraid of a little blood (or a whole lot LOL). He always made sure to let me know he didn't find it disgusting and was perfectly fine with being near my blood. He still doesn't mind, but I rarely do have a flow. My period hasn't stopped him from doing anything sexual with me. I'm comfortable doing it during that time unless I'm having pain, which I did most of the times because endometriosis and IBS make for some hellaciously painful cycles. Had he not been so comfortable with my bein on my menstrual cycle though, I think I would've felt embarrassed, which really isn't necessary. Nobody should feel embarrassed over their period, but I understand if a girl just ain't comfortable herself having sex during it. But guys I'd been with prior to my partner have shown extreme disgust over anything to do with menstrual cycles and that's nonsense.