From the spec,
The
var()function can be used in place of any part of a value in
any property on an element. Thevar()function can not be used as
property names, selectors, or anything else besides property values.
(Doing so usually produces invalid syntax, or else a value whose
meaning has no connection to the variable.)
So no, you can’t use it in a media query.
And that makes sense. Because you can set --mobile-breakpoint e.g. to :root, that is, the <html> element, and from there be inherited to other elements. But a media query is not an element, it does not inherit from <html>, so it can’t work.
This is not what CSS variables are trying to accomplish. You can use a CSS preprocessor instead.