I haven't stayed at the hotel so don't know how bad the noise is, but regarding the construction the Changi website says:

"CAAS has embarked on a S$240 million project to upgrade Terminal 2. The major improvements would include extending the transit area to provide more space for shop concession, passenger lounges and other amenities to cater for higher transfer traffic, and providing a lively and cheerful building interior. Construction work is currently in progress and would be completed by end 2005. "

So it is likely that construction will still be going on in August.