No. Basically, anything that provides and airtight seal and allows you to move the mpc on the neck and keep the seal should do fine. A couple of wraps of plumber's teflon tape should work fine as a stop-gap measure. Duct tape might bleed adhesive and make a mess, though maybe not in a short period of time. Even a strip of paper wrapped around the cork is fine as a temporary measure. Another thing you can do is to put cork grease on the cork and then heat it with a lighter (but don't burn the cork!). This will make the cork expand, but it will recompress rather easily, so it really should be recorked.
A "permanent temporary" fix is to wrap thickish thread around the cork--enough winds to build it up to a point where the mpc fit is snug. But thread is much less compressible than cork, so this will probably not work if you use different mpcs of different shank diameters.