It sounds like you should be fine.

I personally am not a big fan of shake down cruises for myself. I took off on the Trans America as a first tour, but had a lot of other self supported travel experience (backpacking, canoe camping, etc.). That said it is probably a good idea if you either don't have the experience, or just want to do the shakedown trip.

I don't think a spare tire is necessary. I have never carried one and have crossed the country a couple times and done other long tours. A spare tube or maybe two if you feel the need and a patch kit. In goat head thorn country two can be a good idea. You could take some kind of tire boot, but I figure I can improvise one if necessary (I've never needed to on tour).

I typically don't start out carrying food other than a very little on tour and shop daily usually late in the day if possible. I may start out with a few granola bars and some items that are light weight that I may not be able to find on the road. For example I like bulk packed freeze dried peas, freeze dried refried beans, and dried banana chips from Honeyville Farms. The peas and beans are really light. So I sometimes take a little of one or more of those from home.

Definitely don't let it stop you if your buddies bail and have a great trip.