One time, YEARS ago, I had a free ticket booked on NW (not an award ticket - the old VDB free tickets - oh, the good ole' days), and, they had a schedule change, and for some reason, the only way they could get me (oddly enough) to CUN, was with an overnite in MEM. Since it was their schedule change, they offered me a hotel.
That said - - -
I see 6 ATL/CUN flights a day and 8 on Saturdays.
I see 8 TYS/ATL flights a day.
I seriously doubt that with all of the possible flight combinations you could have chosen, that they would pay for a hotel.