poriferans (sponges) are some of my favorite animals
yes its a sponge.
yes most sponges are(can be) very sensitave to air contact
it may or may not kill the sponge depending on pore size and if you can purge trapped air out of the sponge when you place it in the tank. air kills sponge by blocking the channels that water passes through, the flaggela inside the sponge are incapable of pushing the air out.
and yes again sponges are/can be some of the most noxious and toxic creatures when expiriencing die off in tank. some are quite toxic some are just a mass of rotting mesohyl and other fancy names for sponge flesh.
the specimen your holding is a type that is fairly hardy with a medium/large pore stucture, so purging air from it may be as simple as submerging the rock then pressing on the sponge with your fingers to squeeze air out.