Yes, I believe they can depending on the dog and the dedication of the owner. Copper just turned a year old. I would say he is about 95% housebroken. I was told that with small dogs it could take a year...that seems to be true in our case. Most of the accidents we have had in the last few months have been because I wasn't paying attention when he wanted to go out or because of the terrible rains we had recently. I hung a large plastic cat ball attached to a ribbon on the outside door handle. Copper rings it with his paw when he wants to go out. Of course there are times when he just wants to go out and play...but it works pretty well most of the time.
Good luck with your training. Consistancy is the key.
Don't give up!!!