Will slightly loose bearings result in damage?
A bearing that is adjusted too tight can actually seize completely. This happened to me once. I overhauled my front hub and tightened the bearing cones too much. Result: a front wheel that plain stopped turning at some point. 

Too tight adjustment will exert more pressure on the cones and cups, and will probably wear out the bearings faster than too loose an adjustment. 

For proper adjustment, the Park tool website has good instructions: http://www.parktool.com/blog/repair-help/hub-overhaul-and-adjustment