Well the problem is that he didn't really come that close. He never took Edinburgh castle, and not enough of the Scots rallied to his cause. If he went too far south his supply lines would have been quite extended, and the Hanoverians would have kept raising more troops.
Now, I don't think that it's impossible for the Stuarts to have more success at this time. But I think to do so you'd need Charlie to show more strategic and tactical ability than he did, and for the initial landing in Scotland to have more success. If they'd somehow taken Edinburgh castle and generally been able to secure things north of the border its not inconcievable that more of the Lowlanders would have taken his side.
I think it's unlikely that Charlie wins out right and reclaims the throne, but it might be possible for the Union to be dissolved. However, he would not have been happy with this- he wanted England, Scotland, Ireland and Wales, not just Scotland. For that to happen you'd need some kind of convincing French victory on the continent that leads to them dictating terms to George II- and to their client.