They are starting 3 days ahead of you and finishing one day before you. Do you actually foresee overlapping the tour, which will have a three-day head start? If so, expect possible tight camping conditions if you stay where the tour stays. One day last year I stayed at the same commercial campground as Adventure Cylcling's Cycle Montana ride. Things were a little tight, but manageable. Ended up running into 3 people who had done ACA's Cycle Vermont in 2010 when I did it. (Talk about a small world.) And I got a free breakfast the next morning courtesy of the tour. Other than that, expect more people on the trail and possibly crowds a places like restaurants, etc.
BTW...It would be bad form to "sneak" anything. Ask, and maybe offer to pay a few bucks for something like a shower. You never know what courtesies might be extended to you. When I stayed with Cycle Montana I could have easily set up my tent and not paid. With so many people, the campground owner would never have known the difference. But that would have been theft. Not my sort of thing, so I went to the office and explained that I was on my own and paid the $12 fee.