It's true that the yeast keeps working a bit even after FG is reached, to clean up diacetyl and other by products of fermentation. That process takes hours to days, though, and not weeks.
I normally keep beers in the fermenter for less time than a month, like about 10-14 days. That is enough time to give me the results I want. Others prefer a longer period in the fermenter. There is a difference in the flavor that some people prefer, while I prefer the flavor when it spends a shorter time on the yeast cake.
You could try it both ways, with two different batches and see which result you like better.