In short - yes - the play will damage the hub - the more play in the hub, the quicker the bearings will wear and deteriorate and the worse it will get. If you're going to the hassle of disassembling a hub, I'd always dump the old bearings and replace them with new, virtually regardless of their state - bearings are cheap, your time is valuable

Clean up the bearing cups on the hub and the faces on the cones and look very closely at them in good light - are they nice, shiny and generally, perfect? If not, get some new cones from your LBS. Hub races are more of a problem... Finally, when you reassemble, pack the bearings in *lots* of grease. Also, clean and grease the threads on the cone and axle end you're working on - this will make final bearing tension adjustment a little easier.

If the bearings, cones or cups are less than perfect, the rotation will never be perfect - the less perfect the surfaces, the harder the adjustment and the less perfect the end result.