it's not okay to afk farm for 30 minutes, any respectable player doesn't sit around and leave his team to die while he farms the whole game until he has items.
if you waste your gold on items that do not increase your effectiveness early, you'll be stuck playing 4v5 for the most part of the game, and if your opponent is decent and work together, you will lose.
In fact the general consensus of hardcarries is that you shouldn't expect them to help much, but they will jump into team fights if the opposing team is pushing hard.
But they won't come out of the jungle/lane to help you gank. Farming well is the priority of hard-carries, and if there is a good farmer on your team, it's your job to drag the game out as long as you can for your carry to be strong enough to really have a huge impact on late game. It's also your job to try and not lose a 4v5 game - don't try to push rax in 20 minutes, but make sure the enemy doesn't get into your base before 40 minutes.