I can't think of anywhere that you would be able to store it (maybe with Bell Services?) - you can certainly ask Valet when you park, though.
The one thing I can think of would be, if you plan to unpack, put the empty suitcases back into it. That way the clamshell won't be empty if you leave it on the car, and you won't have to find someplace to store the suitcases in the room.
Otherwise, you may need to find somewhere in the room for the clamshell. We were in a BCV 1-bedroom in March and the walk-in closet in the Master wasn't terribly large, When we were at VWL a couple of years ago the master closet was plenty large for something like that but the BCV closets are smaller (I think it has to do with the slight differences in room layout).
You know, I would actually suggest calling/emailing Member Services or the Beach Club desk and ask before you go. If it were me, I'd rather know for sure before I got there.
Mur!