Maybe, to some degree. I don't think this is entirely answerable with the information we have. But we can set limits on the possibilities.
Morgoth, as a (fallen/former) Vala, could have had some knowledge of the future, at least in the early Ages of the World, since he experienced and participated in the Music of the Ainur.
On the other hand:
-he didn't pay much attention: "Little he knew yet [in the time of Feanor] concerning Men, for engrossed with his own thought in the Music he had paid small heed to the Third Theme of Iluvatar" - Silmarillion ch. 7, "Of the Silmarils and the Unrest of the Noldor"
-Men are not bound by the Music, having "a virtue to shape their life [...] beyond the Music of the Ainur, which is as fate to all things else"
So a clear and complete knowledge of Turin's future actions would not have been available to him, but he might have had some idea of the possibilities.