Should I add chat box to my forum?
I’m a big believer in letting the forum be your “chat box”. There isn’t any reason to add another place that members should chat; all chat should be on the forum itself.
One thing you can to to make sure that your members stay and “chat” is to have a general chat on your forum, in many cases this maybe your largest section on your forum.
Also I would not allow members posts to be counted in this section either. Most members may (do) use this section just to pad their post counts.
So no, I would not add a chat box to any forum under any circumstance.