Let's see... it goes something like this...

Speed loaded barge as you wait for the tide,
Faster! the Germans pray;
Tearing their hair and trying to hide,
"Mein Gott let us get avay!"

Anne's rightful heir rides into the Town
And cheering rends the air;
On that noble head sits his rightful Crown,
Above his face so fair.

Speed loaded barge as you glide down the Thames,
Faster! the Germans cry;
Wringing their hands and singing their hymns,
All plans now gone awry!

Etc.

(Of course with apologies to Sir Harold Bolton, Bt., and Miss Annie Wilson (Lady MacLeod), who wrote and published "The Skye Boat Song" in 1884.)

Had the Stuarts succeeded in 1746, in all likelihood Charles would have succeeded his father (James III) in 1766, having married a Protestant princess, and produced an heir-- failing that his younger brother would have done the same and succeeded as Henry IX in 1788, and the line would probably have continued down to the present day, the Duke of Bavaria included.

All of this is, of course, idle speculation. What happened is exactly what happened, and the world is probably no better (or worse) as a result of it.