I would wonder how much power or space it would take. . . being the caveman that I am, I have no idea.
Now, as far as 'Shout Boxes' go, I do have experience on a forum where one is used, and have found it both fun and useful. I would only wonder if whether here, on JREF, it wouldn't be overtaken by some who do a lot of talking. . . I mean as in music related topics--although on that other forum, a member is allowed only 5 shouts per 24 hour period.
The 'Shout Box' seems to be a space between a Chat Room and the regular Forums on a board. In that sense, it gives a full, rounded out range of communication mediums. (and interesting thing, on that other forum, having joined (and JREF had been my very first, and foremost) I pointed out the Chat Room, and some other members who had alread been there, had never noticed it. . . that's because so very, very few had obviously used it. Now, it is no longer available. )
My vote, actually, would be to keep the Chat Room, advertise it a little (not literally, but as Uncle Frank and some others used to do) and educate all members about it's being ok to stop by, say HI, ask a question {or just read, for all that}, or whatever, and then leave. There is no obligation to stay and talk. I think that fear or concern, may keep some away. (although I would hope all would at least say 'BYE' before they left.)
I think, Pavel123 san, that if you went and hung out there a little bit, someone would drop by from time to time. . . but you may not be able to expect too much.