You definitely want it to be heated back up into the fermentation range. I know that when Avery made their Brett IPA they did something similar. Added the Brett to the keg, seated the lid, and then allowed the yeast to carb the beer. I can't see why the beer already being carbonated will hurt it.
As far as having a life long Brett keg, I am not positive, but I think it will be ok. I know Brett has a knack for permantly infecting bottling buckets, wood casks, plastic fermentors, basically anything that can be scratched or is porous. But if it is a SS keg or glass carboy, if you clean and sterilize well, you should be ok. (I think)