Will "Restore" delete apps that are no longer supported?

I have a iPhone3GS (6.1.6) with a functional topo map app "Canada". Whenever I sync the phone, iTunes displays a message saying that the app "Canada" was not installed on the iphone beause it requires a newer version of iphone software. The app website says that the app requires IOS 7.0 or later. Under the "apps" tab in iTunes, the "Canada" app displays a note to "Update". Nevertheless the app still works on the 3GS, and there is no notice on the iphone app store that the app needs to be updated. My question is: if I "backup and restore" the iphone (in an attempt to improve battery life) will the restored version include the still functional app "Canada" or will it be deleted because it was "not installed" in the latest sync?