From what I was able to gather, yes, she does. From a Q&A,
Murata : Hahaha there is no such setting about no panties
According to Murata, few years ago the animation team from Madhouse asked him whether Tatsumaki is wearing any panties, to which he answered she does.
The webcomic also depicts her wearing one and King even sees them.
While the images in the manga might seem to contradict these statements from Murata himself, she could be wearing a type of underwear similar to a C-string or G-string, in which case it would make sense that it's not that visible to the point that she doesn't seem to wear any. Murata never stated what type they were, after all and even joked about planning to use ONE's 'diaper-like' depiction of her panties when he will draw that particular scene someday.