maybe
but at that point it would also mean she lost, and that man is driven
Evil Wolf
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he likely isn't trying to threaten her, but force her to show her hand.
she is a demon, and from the little information we have about them, they aren't particularly viewed in a positive light. so by whatever he's trying to do (menace, assault, magic weapon, hidden mark of the demon) he likely will try either to force her to drop her disguise, or do something only a demon is known to be able to (like say, impervious to physical damage). this doing, whatever happens to him next, he will have already won as she then would lose everything, her standing, associates, support...
could be yes, off screen actions have some tropes like that around them so it seems intentional
but i am certainly not privy to any more information so i am speculating as much as you, but most character actions seem mostly realistic base on what we know of the world and story (with Nameless being the most irrational)
this could also be that the story is arranged for us to "see" through the eyes of nameless, and one big thing is she doesn't trust lady wolf, or most people for that matter.
the unwillingness to bring her out can be easily explained that, their merry band isn't exactly the most welcome in town, especially with the new captain of the guard and the general current situation