Has a good chance. But are you sure its a birch - not easy to see the individual leaves but they don't look like birch to me from what I can see by enlarging the photo..

Agree it doesn't look like a birch... whether the tree survives depends on how much root damage there was when the wind blew it over.

It's White Poplar (Populus alba). It's a common landscape tree in northern Arizona. It looks like the trunk was badly damaged at the base before the wind knocked it down. The roots may have been weakened by that, making it easy for the tree to fall. If there is still enough energy in the roots, it will sprout a million suckers, and one of those can be trained into a new tree.

I just read it grows to 15 metres, thats very big have you the room?....just checking