I would be very surprised if a guest can add a room on to their res at check in, with a dining plan.
The dining plans are a part of WDTC packages, which have to be paid prior to check in.
I would think adding extended day(s) on to a Disney res with dining would require the addition and payment to be made no less than three days prior to check in. That is what I would expect. But certainly could be wrong as I have not personally done this.