it is stated many times in the A|Club Terms and Conditions, that ALL "Adagio Access" and "Ibis Budget" do NOT participate in the A|Club program.

http://www.a-club.com/en/terms-and-conditions.pdf
(on page 2, "3. HOTELS PARTICIPATING IN THE PROGRAM")

and also in the Exception List

http://www.a-club.com/en/hotels_exceptions.pdf

From my understanding Adagio Access is even less "luxurious" than Adagio. Same accounts for Ibis Budget, being an even more elementary and cheaper version of Ibis,... more like a Motel than a Hotel.