letsgetit,
As frantic said, your chances of not getting a GC are as good as your chances of getting into a major accident. Now tell me, are you going to make all your decisions based on the probability that you may have a major accident in future ? Come on, everything has pros and cons.
To answer your main question, yes the bank will take the house if you declare that you don't have the money to pay the remaining balance, but they will calculate very low sell value and they will demand you to pay the rest of the amount. If you can't pay that amount, then your account will be reported to collection agency. You can always sell the house yourself for a better rate than what the bank calculates as the value of the house.