Does convoluted use of language negatively impact a work reviewed by a committee?
How often - if at all - professional academic reviewers face this
issue?

All the time.
(as a side note - there are very few &quot;professional&quot; academic reviewers because in general academic reviewers are not paid).

If they do, will a thesis or paper ever face problems due to language
usage?

Very, very, rarely. For a start, what you see as pedantry, many will see as precision, and precision is the lifeblood of academia. Indeed, this need for preciseness often leads to what you might think of as &quot;mannered&quot; language in an author of average skill. And academics are selected for their skills in their chosen field, not their abilities as writers.
But there is nots of unnecessarily dense and uninterpretable language in academia that isn't tied to the need for precision. Generally a reviewer is asked to review the intellectual content of a work, not the way it is expressed. In general it is only acceptable to reject a scholarly work as a reviewer if the language is so poor that it literally cannot be understood. A reviewer might point out that there are many mistakes of spelling and grammar in a piece, and request that they be corrected before publication, but thats not quite what you are talking about here.