We biked up at Acadia several times, including by tandem. In fact, our first tandem was a rental Santana that I bought at season's end in 1994 after we had rented it from Acadia Bikes!

Anyway, if you are a light team, 28mm might be ok. I'd try to go with 32 or 35mm, though, to be safe. The carriage roads are not paved, but generally are in pretty good condition, although you might find a "soft" section here and there. They are definitely worth a day or two (or three) of riding, though. Very pretty and well laid out. The park loop road is also nice to ride if you don't mind some ups and downs (well, to be fair, the carriage roads are not flat, either). The Loop Road is one way for the most part, and has a good shoulder. It can be very busy in summer, though, especially around the more popular sights, where the shoulder can be taken up by parked cars. Try to ride it early to beat the traffic.

The main park roads are pretty tight, and again can be high-traffic. Nice in the early morning or later in the day once folks go home.

In short, Acadia is well worth a visit, and doing so by bike is one of the best ways to see it. Be sure to pack along a lock so you can secure the bike when stopping to look at the various sights, as often you will have to walk down a path or otherwise be out of sight of your bike to see what you want to see. (Example: stopping for lunch at Jordan Pond.)

On Mount Desert Island itself there are a lot of really pretty and almost traffic-free small side roads, especially on the western side of the island. You could spend many days riding around the island without seeing many cars, as long as you stay off the main highway (Rt. 3) between Ellsworth and Bar Harbor.