Yes, I think they would tack on the extra day...
Its always a judgement call for me which lot to use - I find the big lots to be very convenient and easy to get too - sometimes even walkable...but I dread coming home to a car covered in snow, so if the covered parking is open and the weather forecasts suggests snow, I am usually willing to pay the extra for the convenience of not ruining my vacation feeling instantly upon returning to the car for snow removal!
We apply the same theory to boston as well and routinely pay 200$ to park for the week to be in covered central parking...(the manchester shuttle bus is SOOO much better than the boston ones to economy parking!)