Some previous threads first:
http://www.reddit.com/r/AskHistorians/comments/14f8ui/were_spartans_gladiators_and_other_warriors/
Edit: all that time searching and its in the FAQ http://www.reddit.com/r/AskHistorians/wiki/health#wiki_did_people_in_the_past_exercise.2Fwork_out.2Flift_weights.3F
Secondly, Arnold is quite open about his steroid use (legal at the time), so as far as somebody like him no. It's worth noting how he used steroids though, he didn't use them while gaining weight but did use them while cutting fat, which maintained his muscle, so a guy as big as Arnold isn't completely out of the question, just not one that's both as big as him and as low in bodyfat.
Arnold is exceptional even by Hollywood standards though. These three are more in line with it (For context, they performed a circus act called the Saxon Brothers focused around showing feats of strength, pre WWI). They were around before performance enhancing drugs were a possibility, though they had access to barbells (not like a modern one, these had a hollow metal sphere on each end that could be filled with sand).
The Greeks certainly understood the concept of picking up heavy things though, there are stones that people wrote their names on as accomplishing lifting, for example the Bybon stone weighs 143.5kg and claims that Bybon lifted it overhead one-handed. They also understood progressive overload, the myth (mythohistory?) of Milo tells of him carrying a calf every day, and as the calf grew into a bull he got stronger.
A more interesting question than if they could, is if they would want too. The very low bodyfat that a six pack implies is a potential liability for a soldier because of a lower tolerance for meals not showing up, and a bigger body means needing more food in the first place. Even if the food supply is solid the former could pose a problem. Top level MMA fighters often don't have well defined abs despite the regular supply of food and pressure to keep light enough to make weight simply because a certain amount of bodyfat is needed for peak performance.
Also there's a question of proportions, the modern Hollywood guy typically grows his upper body muscles most, arms, shoulders, chest. But this amphora shows hoplites with big legs, not big arms.