I would expect that special symbols such as $ and \frac{abc}{def} are excluded from the character count in comments. So that \frac{abc}{def} counts as just 7 characters instead of 15. And similarly $1$ as just 1 character instead of 3.
Because maybe this discourages use of special formatting in comments. Not sure if this is intended behavior or a known issue.
This is certainly not a bug. As mentioned in comments, character count for other formatting options is also by code and not by output. For example **1** is counted as five characters, although it is only rendered as 1. Similarly [a](http://spaaaccccce.com/Space_going_to_space_cant_wait_Oh_oh_oh_This_is_space_Im_in_space_Wanna_go_to_space_Im_going_to_space_Gonna_be_in_space) will count as 147 characters, but again is rendered as a single character. And this goes for magic links in comments, too, where the four character [so] renders as the fourteen character Stack Overflow.
And this same methodology is used to count characters in posts, too.
The strict character-length limit on comments is there because comments are not intended to convey a lot of information. They are meant for requesting clarification from the author, leave constructive criticism that guides the author in improving the post, and adding relevant but minor or transient information to a post. If you are posting a comment with a lot of MathJax that brushes up on the 600 character limit, there's a good chance that you are using comments for something other than their intended purpose, and you might want to consider either posting an answer (if you comment is an answer), or editing the post (if the comment is clarifying part of the post), or posting a question (if the comment is really asking a new question).
As an aside, to a certain extent it is an accident that MathJax renders in comments at all. Across the network only a very limited subset of MarkDown is available to be used in comments: bold, italics, code and links. On MathJax-enabled sites, MathJax is rendered throughout every page, and is not restricted to posts, titles, and other elements one would expect MathJax. This allows MathJax in comments, but also sometimes forces MathJax to render where it should not: for example, question titles in the Hot Network Questions list from non-MathJax-enabled sites about money might be rendered as if dollar signs were MathJax delimiters.
*A*displaying as A also counts as three charactes. It would also be hard to decide what to do exactly instead, leaving aside that it'd be hard to implement, too. How many characters exactly for $\sum_{n=1}^4 n^2$? To discourage overly long and complex comments is actually desirable. $\endgroup$${}{}{}{}{}{}{}{}$$\endgroup$