Do you think the Union army during the American Civil War would be able to win the war if they hadn't win the battle of Gettysberg?

Perhaps. It depends on how badly damaged the CSA army was, too.

Almost certainly.

Gettysburg came to late in the war to save the south IMO. Depending on the scenario (ie when Lee defeated Meade during the battle) I still doubt Lee could have forced the North into anything. His main chance rested in either outflanking Meade at the start of day 2 (ie before the casualties mounted to silly levels) or in manouvering between Meade and Washington and forcing Meade to attack him in a position of his choosing, ie what Longstreet asked for. Even despite all this, Meade's army was unlikely to have been totally destroyed in the Gettysburg engagement, and between the AOP, Washington's defences and the Union reserves, Lee would have found it next to impossible to capture or pressure the city.

What it might have done though was to affect the upcoming 1864 elections, which, had they lead to a McCellan victory would almost certainly have lead to an end to the conflict, even if it meant the south being given independence.

Probably. Gettysburg was the turning point of the war, but, by that point, the South couldn't afford to lose any major battle. It was bound to happen eventually. The North simply had a much stronger war machine and a prolonged war was not in the favor of the South just like Japan in World War II. Eventually, Northern industrial might would overcome the Southern tactical advantage of having better generals. Throw enough troops and bullets at the problem, and it will go away.

That battle also allow Lincoln to free many slaves and add man power to his army. If he were to lose that battle, freeing the slaves would look like a desperate attempt to gain man power. But perhaps more importantly Gettysberg ended British talk about supplying the South. I don't know if it did directly, but the idea ended after Gettysberg. Would the British give up the idea of supplying the South if the South has won Gettysberg.

The British supplies would not have made enough of a difference to counteract the Union superiority. Britain's support was only ever lukewarm, her intervention would have come 5 seconds after the south no longer needed it for example :D I'd say that British drop in support relied much more on factors such as emancipation than victories, the British did not want to be seen supporting a slave nation in a war it was destined to loose against a slave-freeing nation. British imperial hypocrisy didn't quite stretch that far ;)

No, all Gettysburg would have likely achieved would be to pressure the North and Lincoln overall, damaging his re-election chances.