If the leaver leaves early enough, you can have a major advantage on your hands.
There's less exp/gold to split. If your team takes care of it right, you will have a strong power advantage till about 34 minutes in. Not sure if this number has changed since all the exp and gold changes, but it's certainly a thing.
The only rough part is that they will have superior map control, so long as they do that right. And if they do it right, which is rare, they can stop you from ending the game with your mid-game advantage.
Of course, the entire way you play the game has to change. If your mid-lane DC's, you don't just shove the jungler mid and just play like you don't have a jungler. You're wasting all those jungle camps and providing infinitely less pressure. You need to rush the forget out of a tower or two, force laning to end, even if it means giving up one of your own towers.