Sure, he could warg into the Nigh King in the present while greenseeing in the past. The Night King wouldn’t start looking like Bran as a result, the changes would be to the Night King in past and future and not to Bran.

Breaking Hodor/Willis’ mind happened because of the connection and an odd combination of situations under stress, it wasn’t designed or predictable. Is it possible sure, but it still isn’t time travel.

Unless, that is, if Bran got lost in the warging the Night King, in which case, the Night King wouldn’t look like Bran, and Bran wouldn’t be talking as Bran to Littlefinger, Arya, and Sansa coherently.

Occam’s razor suggests that NK has some or all of the same powers (and might be a historical Stark).

I was answering a specific theory, not suggesting crazy other things weren’t possible.