That has never been my experience. I tell the front desk when I check in that I have two reservations for consecutive nights. They always make a note of it and they do the "check out" and "check in" on their own. I have never needed to go to the front desk again, though often before/after breakfast or on my way out of the hotel for the day I do mention it (never has been required or necessary though, per the front desk).
I have had to go to the front desk four of the five times I have extended using Priceline.
One time we needed to extend a night, my wife was able to talk to the hotel direct and get the stay extended at the Priceline rate +$10.