No he cannot grow to any size but neither can Hawkeye without the help of Dr. Pym's chemicals. On the other hand Oliver Queen's powers, if any, remain unknown. It has been rumored that Green Arrow may in fact be a metahuman. The Department of Extranormal Operations has a classified dossier on Queen, wherein they indicate such a possibility, but as of yet, this information has not been confirmed nor denied. Besides you said Hawkeye not his Goliath persona
, in any event size doesn't really matter, I am sure like me you have seen heroes defeat other characters bigger and more powerful than them all the time in both Marvel and DC Universes.