I did, but it wasn't exclusive. I only told people who asked where I was registered that were tech-savvy (e.g. not my relatives). It wasn't listed on the invites, just the brick and mortar store.
DH's coworkers mostly ordered off it and it seemed to be no problem. Although I did receive one "mystery gift" as the receipt indicated the sender had ordered hdmi cables, when we received the requested cloth diapers. I found out 6 months later who had sent it to me.
From the other side, a friend registered from Amazon for her wedding and I really liked being able to see what she thought she really wanted vs. what was nice to have. And considering I couldn't attend her wedding, I didn't mind paying shipping charges since I was going to anyway, although that can be a concern for some guests.
Short story long, it might get complicated, but I'd register a couple different places anyway. And if you don't have a BRU or BBB, Amazon might be a good choice.