Does a research group actually review every applicant's documents in case of overwhelming number of applications?
When I get applications to review, I usually do a pre-pass on every application. I look for GPA, test scores, and compliance with requested application materials (i.e. did they even have anyone write them letters of recommendation?). We usually have explicitly stated bottom line cutoffs for GPA and test scores. Those falling below these marks are automatically set to the side. 

I next try to scan the research statements / statements of purpose. This eliminates a large amount of the candidates usually. 

I then cut the remaining applications into about half. I select who I want to accept from this half stack and order them roughly from strongest to weakest. I then do a spot check to see if anyone in the other half stack is clearly superior to the weaker candidates in the already selected stack. If so, I do an insertion of the new candidate and the weakest person is dropped from the list. 

In the end, yes, I've looked at everyone's application, and no, I have not given heartfelt and deep thought to each applicant. 

We then send out an accept/reject form email to every applicant. I very rarely even reply at length to students who fight their rejection.