Yeah it's called Forum and it will usually have a huge F on the base In all seriousness I've never seen a fake board, and if they do exist you could probably see them on Craigslist or ebay, but I really doubt anyone is taking the time to make fake Burton boards.
I haven't heard of anything like this with snowboards but anything is possible. If you know snowboards, you should be able to tell by the build quality, flex , etc. Other than that, it would be prety tough. Boards are prety expensive to make though and I think it would be difficult to produce and distribute phoney Burtons. Thus I don't think it would be terribly profitable.