Should be quite easy. Buses and trains start running downtown around 5:30 so plenty of time to get to your bus. If you're at the Hilton, just wander over to Terminal E and take the Silver Line to South Station (15 minutes) and the Red Line to Park (5 minutes) where the buses board. From the Hyatt, take a shuttle bus to the Blue Line and take that to State which is a five minute walk to the buses, or take the water taxi across the harbor and then hoof it 10 minutes to Tremont. The Embassy Suites is just off-airport but a five minute walk to Maverick on the Blue Line, which is a five minute subway ride to State. With waiting time and walking, it's probably 20 minutes from the start line.
There are other hotels that bill themselves as being airport hotels but they are often quite a bit further away. For those, if they're close to the Blue Line, you're probably fine. If not, avoid.
One hitch is that Government Center Station is closed for repairs, so to get from the finish to the airport you'd want to take the Orange Line from Back Bay, but it's just as close as any (open) Green Line station to the finish. Oh, and it has escalators.