Not necessarily. It'd be for how he views himself. While the shapeshifters kinda' explore the concept in some episodes, it may be fair to assume they identify as they present, because they can literally present how they want.
Granted, I could see Odo having some odd identity issues with presenting to please others or over duty to his job more than personal identity given his upbringing...
Did they explore his gender identity in that episode(s) or did they leave it all allegory? Ugh it was so long ago... Maybe time for a rewatch.
As far as I know, Odo is a masculine Shapeshafter.
It also use the identity of the one who study him, it was his choice to be like that most of the time.
He present male and has had relationships with women. But he can present any way he likes. And the founders maybe don't even have gender.. so not even binary.
What definition is that? Assigned nonbinary at birth? The fact that he could choose to present as nonbinary but presents as male is pretty telling, imo.