Don't listen to the nay sayers. Load up lightly with a saddlebag and handlebar bag and have a good time. The Trek Madone 4 is a "plush bike" and will work if you are careful with your gear; you sound as if you are planning that pretty well. Definitely get a Hosteling International card. I stayed at a load of Hostels during my last trip to Iceland and they were very comfortable. You might also look at sites like warmshowers.com and other home stay resources.

I've been touring on a steel sport tourer with a saddlebag and handlebar bag for years and many people do it with even less. I'm going to be trying it on a Cervelo RS soon so I don't see anything wrong with the Madone 4 if you approach things sensibly.