That's a bit like asking if getting a new stereo will make your dead car run again.
I'm not being sarcastic, but the Flash Player CAN'T solve problem with the messed up code of the browser. Microsoft needs to fix IE. It isn't an Adobe product, and Flash Player is only a plugin for IE, not the other way around.
If Microsoft doesn't fix their browser, even Flash Player 13 (whenever it's released) won't even make it work.
I could never stand the garbage Microsoft calls a browser, and I only use IE for testing. Just because IE comes with Windows doesn't mean it's the only browser there is... and it certainly doesn't make it the best choice. In order of preference, I recommend:
ANY of those will work where IE11 won't, with the Flash Player Plug-in (For all other browsers), and Chrome doesn't even need that because it has its own Flash Player plugin built in.