I did a brute-force search on all two-letter words allowed by the scrabble rules, and there's no strategy that can win with every word if 7 errors are allowed.
That's probably not really relevant as no one would allow two letter words in hangman.

But I also ran my algorithm on 15-letter words, and there, winning is possible every time with a maximum of two mistakes!

In the more common word lengths, such a search quickly becomes impracticable, because there are just way too many words.