Yes ...BUT it depends on just how much it has defrosted..Slighty and there will be little loss of quality. If it has liquified...then no,as the texture will not be the same.
Yes I do it all the time. It is not a good idea to refreeze home made ice cream as its made with eggs but the stuff you buy from a supermarket is nothing like that. The quality will be slightly affected by the number of times you freeze and refreeze the product but it should be fine to eat.