Could the Confederacy have won the American Civil War if they had managed to get Britain to interfere on their side in 1862?
Yes, which is why they tried.
Could they have managed to get Britain to interfere on their side in 1862? No. The Union Cause had mass popular support in Britain and any government trying to interfere on the Confederate side would have fallen within the week.
I guess some kind of Zimmermann Telegram by Lincoln might have done it...