Adultery according to IPC 497 is
(1) Man should be married.
(2) His partner woman should be married.
(3) Adultery is committed w/o the partner's husband's consent.
If these three criteria are met then only it's a criminal offence and it does not matter if the man is awaiting divorce for whatever reasons.
So in the case you mentioned, it's not an adultery from criminal point of view.
But not sure if living in is allowed. I guess it is.
But note that prolonged living-in is considered equivalent to marriage. I don't know what the definition of "prolonged" is but with little care the man can easily prove that the relationship is not very old.