I think if Burnham was a man, it would somehow make the character even more annoying.
In my opinion, there's a difference between a character being unlikable and simply annoying. The latter, when unintentional, is often a product of writing inconsistencies. Burnham seemed driven by her emotions, which felt inconsistent with her being a graduate of the Vulcan Science Academy. Given her backstory, I'd expect a highly professional, balanced, and logical character. Her actual character was hard to reconcile with that. Maybe she gets better in later seasons, haven't watched past season 3 yet.
There is a whole array of unlikable characters on television and in other media. I think my favorite example of an unlikable protagonist is Yennefer from The Witcher book series. Arrogant, abrasive, manipulative, but extremely well written. Speaking of the Star Trek universe, I'd say Bones was pretty unlikable, definitely Tom Paris, and arguably La'an at the beginning.