This is one of the most frequently asked question by any newbie windows phone developer.
Will the developed Windows Phone 7 App run on Windows Phone 8 Devices?
The answer to this pretty simple and straight forward. Yes, in most cases, the Windows Phone 7 app will run fine on Windows Phone 8 devices. But the only drawback here is that the apps targeting the Windows Phone 7 would not take advantages of the features that are part of Windows Phone 8 like Wallet, NFC etc. . . . The App runs in the Quirks mode in the Windows Phone.
It is also suggested to verify and test the Windows Phone 7 app on the Windows Phone 8 devices. Check the list of the breaking changes from WP7 to WP8 from MSDN