As many people above had said the mat is just as important as the bag itself. I have a thermarest and although it is a little bit more expensive it packs down very small and is very comfortable once inflated.
That bag will do fine for the summer, and as it was free you have yourself a bargain.
With regards to the space I suggest using either a drybag or a bin liner to keep it dry and then attaching it to the top of your pannier rack, leaving more space for other stuff in your panniers. I carried my sleeping bag on the pannier rack on a tour from Istanbul to Paris this summer and encountered some pretty hideous rain, but the sleeping stayed nice and dry inside a drybag:
http://www.sportsdirect.com/exped-waterproof-drybag-710017?src=google
Hope you have fun with all your new gear!
Chris