I have had my spare inside just waiting for my rear tire carrier. I am not sure if the 33 will fit with the tow package, it was very tight without it on. I personally did not even try since my solution will be the tire carrier. The way I see it, spend $220 (or so) on a tow package or throw in another $500 (or so) and get a nice setup with the tire carrier.

If you deflate that spare, make sure you have a good reliable source to pump it back up... whether its a CO2 set up or just a 12V pump.