It's a two-edged sword. A group can pull you along, but trying to hang with a group that's considerably faster can cause you to run out of gas long before the finish. Don't over-extend yourself early in the ride.
A 7:40 moving time century is slower than 14-15 mph. It's in the 13-13.5 mph range, if my arithmetic is correct. I doubt you'll be able to sustain 14-15 for a double, even with groups pulling you along. Wind and hills tend to break up groups. Once you're 100' off the back of a group, it's a lot harder to catch back onto it. Your goal is to finish, and have fun. Play tag with the groups that come along, and if they drop you, wait for the next group.And avoid the temptation to try to latch onto a group going 16+.