personally I wouldn't want to get involved with a girl who got engaged to a guy after seeing him for just one month
It shows a distinct mental imparement in my opinion (unless the guy is minted, tripping over his dick or has an 8 inch tongue and can breath through his ears)
sure bone her if you get the chance but I've had my fair share of chicks with issues in the past so IMO the engagment after a month is a big indicator of trouble below the surface.
I was in a similar situation a few years back, I was hooking up with a very sexy but unhappily married chick and became emotional crutch boy/happy distraction/4am texting buddy/fantasy escape, yet I didn't fuck her as I was major AFC at the time (oh boy if we hooked up now she'd be like

lol) and eventually she left her hubby

and totally side stepped me went off and found a boyfriend or two/three over the next year and we don't even talk anymore so lesson learned... don't be a chump, don't let her problems become yours, get her boned pronto or get out now or you'll be wishing you did later I suspect
abort.. abort.. abort