I don't know for sure, but it may be possible. We had the engine removed from our 280 and the yard disconnected lift struts and removed the transom seat and back. They then just lift the cover up and leaned it against the transom with the hinges intact. They did tie the hatch down and when it was done three of them set the hatch back down, one guy attaching the struts the other two holding the hatch.
My '04 300DA (same boat as yours) had the port engine replaced just before I bought it. On the invoice for the work it says "removed drive, removed hatch, removed engine".