If you do that, it will come off as weird. If the feeling isn't mutual, in my experience I've shared what happened with a partner and I was not allowed to hang out with that guy on my own anymore and my partner would deliberately try and make the guy that uncomfortable. They did everything short of pissing on me to show who I was with. lol. That or you'll be the running joke behind between the two... don't be that creep. That never ends well. The fact that you have to ask if you should do it.... says to me that you aren't getting any clear signals from her... it sounds like a bad idea.