should yes, after it expires grasshopper will deactivate, but you can still use it to check through the rhino file. you can of course also work in them further but saving and exporting is deactivated. you can also update the expired Rhino version any time. the expired version will not expire any further, so as a viewer it will always keep working legally till you purchase a license, then it of course will become a commercial and fully working application again.
i think you can use it as a read only app also anytime you cant log in to the zoo but i dont have first hand experience, in any case that function to use it as a viewer should persist at anytime.