I don't think they will kick you out ....
However you may have a nasty surprise on your room bill .....
There is -NOTHING- that prevents them to charge you a much higher rate for the nights beyond the one you originally booked ....
Remember that checkout times are posted everywhere and that you have therefore been notified that additionnal charges may occur for people that checkout late ....
The max they can charge for the room is posted (along with the checkout policy) pretty much on every room door ...

Realize that by intentionnally "overstaying" you are potentially affecting another customer which will have to be compensated by the hotel if they can't give him a room ... therefore the price hike on your bill is justified.

you should call and call again to secure the nights you need up to your travel date ... this is the right thing to do for your wallet, for the hotel and the travelling public...