iPhone 4 stuck in recovery mode while upgrading to iOS 6

I was trying to upgrade my iPhone 4 to iOS 6 when it gave me this error message:

"iTunes has detected an iPhone in recovery mode. You must restore this iPhone before it can be used with iTunes"

I can restore its original settings by clicking on the "Restore" button.  Once I've done that, will I still be able to Restore from Backup?  Or will the initial Restore to Factory settings wipe out my existing Backups that I made through iTunes on my MacBook?   Luckily I Backed up the iPhone (to my computer through iTunes) before I tried to upgrade, so hopefully I can restore it to that backup?   Help!!!!!