Can Pruning Fix a Badly Leaning Apple Tree?

A little bit of neglect has left one of my apple trees with a trunk leaning at a 45 degree angle to the ground. As it is, the tree is throwing a lot of low shoots and is very poorly formed. In a real desperation move, I've decided to cut the main trunk down low and encourage one of the lower shoots to replace it.

I'm really interested to see what happens, and if you're someone with some experience in fruit trees, please let me know your opinion. Is the pruning injury too severe to recover from? Will it begin to send a copious new shoots down near the ground?

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