Nah. Brig wins against Mei clean. Brig has three methods of surviving Mei’s primary fire, and Mei has no means of outdamaging Brig before she dies. Even if Mei self-heals, all Brig literally has to do is stand there and wait and the Mei screwed.
The only thing Mei has that Brig can’t deal with is Ice Wall, and like I tell people about Mercy, escaping a matchup does not mean you win a matchup.