Systems that are gravitationally bound will stay that way, yes. (At least as long as a "big rip" scenario does not happen; our best current observations say it

Systems that are gravitationally bound will stay that way, yes. (At least as long as a "big rip" scenario does not happen; our best current observations say it won't, but the error bars don't completely rule it out.) Generally speaking, the boundary in our universe seems to be around the galaxy cluster level: galaxy clusters are the largest systems that are generally gravitationally bound (although often quite loosely, so that objects near the outer edge of the cluster might fairly easily acquire escape velocity through random encounters with other objects). That corresponds roughly to a distance scale of a few tens of millions of light-years.