Popularity absolutely does not impact the logical correctness of an argument: an argument is true by virtue of its own structure, if you say popularity somehow affects its correctness you've basically jettisoned logic in favour of subjective opinion.

At best popularity serves as a useful heuristic for when you don't have the means to carefully confirm the correctness yourself.

(There is a fairly uninteresting special case where the popularity of something comes in to the argument as a factual statement about the world.)