No, it is not grammatically correct. It should be What do the comments say?
If you want to refer to a particular web-page component, then do so by name or description.
For example: You can say What is said in section Comments? if there is a section named Comments. Or you can say What is said in the comments section? if not (and if there is only one section for comments). The particular section or kind of section is made clear by saying that it is the section for comments. You can also say What does the comments section say?. And you can also say What is said in the comments?, which does not refer to a comments section as such.
There are many ways to correctly say what you want to say. What does the comments say? is not one of them.