The short answer is yes. But the styrofoam has been absorbing steam for over a lng period of time and it would probably take years to dry out completely . Instead clean the cover and replace the water logged foam with sheet insulation that is more dense. You can glue the sheets together to make then the same depth and use the existing foam as a template to cut the new one. Cover the new insert with plastic wrap. Window shrink wrap works well and be sure to covert any small holes you make with tape to keep your new cover dry for as long as possible.
This will take a few hours and save your hundreds of dollars.