Yes, you can feed your tweets to your FB status. It does sometimes imply 'I don't use FB any more' but that in itself could be a good way to discourage people from bombarding you on FB. 

If it doesn't feel too 'celeb' you could always have two accounts; one for the 'author/brand' and one 'deep cover' account for you. That way you can still keep in touch with real friends (but will have to invest a bit of time in maintaining that chinese wall).