Question
If I do not spray the caterpillars on my birch trees, what will be the result.  If they loose leafs soon anyway, and caterpillars fall to ground what happens to them?

Answer
It will depend on which insect did the defoliation. The tree will recover-hardwood trees have the capability of storing energy and leaf out again--late defoliation will leaf out next spring.

Where the insect go will depend on the insect--some over winter in the ground others as eggs on the tree branches. IF the defoliation is a couple of years in a row the tree will lose growth and you might see some branch dieback. IF the insect return next year I would consider spraying or use a soil applied insecticide like Bayer Advanced Tree and Shrub insect control. The soil applied will last all season and protect the tree from defoliation. Here is a web link to this product check with your local garden type store for it.

http://www.bayeradvanced.com/tree-shrub-care/products/12-month-tree-shrub-insect