Apologies,... just saw that you thought "Access" would only be part of the name.
In fact "Adagio Access" is a seperate brand as you can see in Accor's brand portfolio below.
"Adagio Access" and "Ibis Budget" (including "Etap" and "Hotel Formule 1", which will be rebranded to Ibis Budget) are not part of the A|Club program.
However, what confuses me is, whether the regional brands (Grand Mercure, hotelF1, motel6, studio6) are part of the program, as they are not mentioned anywhere in the terms & conditions. Especially for the Grand Mercure properties this would be interesting to know.