@PJH I would say yes they should. One of my previous places had developers only on code reviews, and they always picked out the easy stuff. Bits like inconsistent indentation and poor variable names were the main features of the code reviews.
Then the software went to QA and fell over. Repeatedly and for stupid shit. Once QA joined in the code reviews, and were routinely looking over code they were picking up things like not checking array bounds, not zeroing sensitive memory and other relatively simple stuff at every review.
Having QA involved with the code reviews meant that much more was caught early, and less bugs ended up in test.
/Preaching