If you have the room, Porkpal, you can afford to encourage that. I never had enough room for the rugosa suckers, and they were so thorny!
Liz, by cutting them, you're producing the same stimulating effect that any type of pruning would produce. I'd be tempted to dig up the entire rose, pull off all of the suckers, and re-plant the rose. This is a good time of year to do that.
