Yes, they can. In our Club, we have registered a specific location where we have one or two Club float fly's each year, plus a location for indoor flying (may change, year to year, so we have to re-register).
Unlike bashing around in public parks, etc., the flying at both locations has some controls, i.e., following safety guidelines (as explained in the Pilots' Meeting prior to flying that day), frequency control for 72 MHz, separating incompatible kinds of flying activities, limitations on size/power when appropriate (such as maximum size heli allowed for indoor flying) and just plain common sense. I think that is what having reasonable insurance coverage, at affordable prices, requires. It is not that hard to do. Everyone has fun.
As for flying elsewhere, check your home-owner policy. They MAY cover you. Or, they may say something like, "Are you nuts?"