A benefit would be that your children would get a glimpse of normalcy and seek that normalcy in future adult relationships... neither seeking controllers, users and manipulators nor seeking compliant appeasers.
So... "better late than never" may be a theme that works for you.
I agree with FD, if you were truly on board and ready for divorce. I think if you began the proceedings at his age of 15, he'd be so close to 18 by the time it was settled that custody won't be an issue.
From your post though- you aren't really considering divorce. You are considering calling her bluff by taking her up on her threats. In this regard, you both are not really wanting to divorce. Reacting to her threats to call her bluff will only escalate the situation. You have already stated you are committed to staying married to her.
In the situation where you are going to stay married, and you want to do the best for your son, then- the way to get him exposed to "normal" situations and away from the conflict is to help him to be able to leave it himself. He can't do this at 15, but there are options. One for me was to let me visit relatives during school breaks and I also could visit friends at their houses. Teens spend more time with their peers as they get older. If BPD mother was acting up at home, I could get to a friend's house for a while. I also went off to college after graduation.
This didn't undo the issues I was exposed to at home but I had some distance from it. I also had access to student health counseling to help. It wasn't a solution, it was a start.
Letting a grown child leave the dynamics at home does not mean no relationship with them. As an adult child, I formed a different relationship with each parent- according to each parents' ability to have a relationship with anyone. BPD affects all relationships. This is your time with your son. Since you have no wish to divorce - why spend more time and money with an uneccesary conflict with your wife?
My best childhood memories with my father are when we did things together without BPD mother as he would then be able to pay attention to us kids. Try to make some time to do this with your son.
One thing I needed to learn was to not react as much to BPD mother's threats (to me, not about divorce). She'd make a threat, I'd react and then there'd be conflict and drama. This reinforced the behavior because then, the focus would be on her.
When your wife makes threats, she's pulling your attention to her, and away from whatever else you need to focus on, including your son, who likely is already getting the short end of your attention. Maybe she is doing this so you will tell her not to leave. Surely it makes you feel angry and tempted to react. This is an "invitation to the crazy (drama for both of you) party". It works for her to gain your focus, but you don't have to attend the crazy party. You can stay calm and say "honey, I wish you wouldn't leave" and then repeat as needed.
The choice is yours. If you were seriously considering divorce, the advice to stay would be out of line, but you aren't considering it. You have stated you are staying married and so, considering that, don't call her bluff. While your choice is to stay, it may not be your son's choice, so help him to gain independence so he can one day make his choice too.