Let's say you have a lot of posts....like me I suppose.
I've changed my signature a few times and have not seen much affect on ranking. Where it currently says atlanta real estate blog in the signature, it used to point to my luxury real estate page with the anchor text "atlanta luxury real estate". That was about a year ago I made the change to the link. My position for that page on that term did not ever change.
Whether this is typical or not, I'm not sure. It's not really enough information. However, there is more to consider. Some of these older forum posts are not likely spidered all that often although some may get recached fairly quickly. However, you can make all of the changes that you want, but, until the page is recached, it really hasn't changed. Then there is the question about how long it actually takes for a "new" link to affect the rankings.
So, to answer your question, maybe, maybe not. It would like get a new site cached more quickly.
I wouldn't do it as there is something to be said for the length of time a link has been pointing to a certain place. I don't see any sense in starting the clock ticking on a link all over again.