Generally, no, it won't be a significant difference. But as a rule i'd suggest 2gb if it's a half decent GPU like the 7850.
But it depends on resolution & the specific game as not all games use more than 1gb, in which case 1gb or 2gb wont make any difference. At 1080p ideally you want 2gb, but below this it's less of an issue due to fewer pixels to draw & less strain on the GPU.
It's not worth changing it now IMO. If you want to upgrade, wait & go with a new card.