Was Annael in the battles of the First Age?

[Turin_Turambar]

Annael, Tuor's stepfather, was the leader of a grey elf union in Mithrim in the First Age. It is said that he lived in Beleriand before the Noldor returned to Middle Earth and even fought in the First Battle. So, do you think Annael fought in Dagor Bragollach, Nirnaeth Arnoediad and War of Wrath? There were also grey elves in Dagor Bragollach. And in Nirnaeth Arnoediad, Mithrim elves joined Fingon's union, but only Annael could return to mithrim after the war. I also think it is reasonable that he fought in War of Wrath. What do you think?