Very likely, although I think he would be able to predict something like that to happen and thus would be better prepared.

Oooookay... Trollhunter!Barbara AU where's she's just... like that now, courtesy of @theoldandnewfirm

Umm, dramatic post-battle kiss for Trollhunter!Barbara and Shadowmancer!Strickler?

What if Beast!Barb and Shadowmancer!Strickler...?

(or, if the answer is no, would Strickler straight up kill her since he's smart enough to know that she will always be a threat unless she's dead)

I could see it going either way depending on Morgana's willingness to listen to what Stricklander has to say. And whether or not Strickler wants to have that kind of conversation in the first place.

In my mind he's a lot more confident in dealing with Morgana in this AU, since he takes a firm "Changelings first" approach and remains in control of the Janus Order the entire time. (That's why he has to antagonize Barbara for so long)

Whether or not he and Morgana can come to any kind of consensus will depend entirely on whether or not she is willing to recognize Changelings as equals rather than servants.