There are too many indications that the doctor already had his member by the beginning of Season 3.
The 4th episode in Season 3 'The Swarm' the doctor suddenly went off-line from many visible sub-routines and also the Swarms influence. He had to be re-initialized by the Dr. Zimmerman holo-gram.
Near the end of Season 3 in the 'Darkling', the doctor has another break-down when he's tying different personalities from famous people into his program. He almost kills Kes when jumping off a clift.
Several episodes later in 'Real Life', the EMH created a perfect family(including a wife) to live with to experience perfectly harmonious relations.
This is just before Seven of Nine.