Is 2^65536 + 1 known to be composite?

yes, and it even has a fairly small factor (825753601). see http://www.prothsearch.net/fermat.html for up-to-date information about factors of fermat numbers. according to that page, the next term from your sequence (F_65536) has unknown character (prime v. composite), but they do know prime factors of some larger fermat numbers. mike