The answer is yes to a very very good approximation, but you have to be
very careful to keep the total amount of material that's being weighed
Usually, when a frozen fish is thawed on the countertop (at least
in my house) water vapor condenses on it, first making white frost, and
then it melts, leaving a puddle of water around the fish. The frozen
fish itself may have little ice crystals which will melt and flow away.
You have to make sure that all the little bits of water are weighed
before and after the thawing, and that no extra bits are added, and
then you should get pretty much the same weight. Leaving the fish in a
sealed container from which you can wipe the condensation should help
keep the total amount of matter constant.
There is a very tiny relativistic correction to this -- thawing a
fish increases its total energy, and since E=mc^2, raising E a tiny bit
increases m a tiny bit. But I'll bet this is unmeasurable, given that
even with the most carefully controlled weighing, a few atoms will
sneak on and off, or the scale won't measure to the precision needed.
(republished on 07/25/06)