With that many people in the hand and for a draw I would want to try to see another card as cheaply as possible, you have to remember that AK is nothing more than a drawing hand and can be beat by somebody making a pair of deuces. There are actually better hands to make straights with, such as JT, because with AK the straights can be made only in one direction.
If I was OOP post flop with AK and somebody bet after I checked, the pot odds
would have to be extremely tempting for me to call (such as min bet of 30 into a pot of 300) and if I didn't make anything on the turn, depending on which card came, I would most likely be done putting money into this hand. This would be especially true, for example, with 3 cards of a suit on the board where I don't have any of that suit.
Another thing to consider when you have a bunch of people in the hand like this is a situation where your call does not
close the action, for example somebody bets 1/3 pot, you call, but there are others who still have the option to raise or shove. Now if that happens you're faced with two poor choices; call the raise or shove which would most likely be a -EV move with this many people in the hand, or fold and wish that you had gotten out sooner before you wasted more chips on the hand.
If I was UTG against 3 others with AK and missed the flop, no c-bet 100% of the time.