I cannot see a Stuart Restoration lasting long. If it did happen in the War of Austrian Succession, it would have been because a Catholic young pretender used a mostly Catholic, semi barbaric army to force his will over a country that had most of its army in Europe at the time, with backing from the hated French. Anti-Catholicism in Britain was not a relic of the past by 1745, but was rather state sanctioned and alive and well.
Charles would be no less hated than James II was, and would be trying to control an empire much larger and much wealthier than the one that his grandfather failed to control. The American colonies would not recognize his rule, the overseas colonies in general would not either, and the army in Europe would see it as a stab in the back, while the navy would side with the Hanovers. He might find support in Ireland, though. It is possible that a landing in Ireland might have been a good idea.