If intended, would it ever work what Barney did with Robin in "How I met your Mother"?

When he told her he'd give up on her, whichafter he'd flirt with her co-worker and treat her way better than he treated Robin and thus got her jealous enough for taking him back?

https://how-i-met-your-mother.fandom.com/wiki/The_Final_Page_-_Part_Two