Windows Phone 8.1 has additional APIs to NDEF format previously unformatted tags, as well as to communicate with various smart cards through NFC through raw access instead of NDEF (e.g., ATM cards).
You can get some more information about how to integrate the new NFC functionality from the WP 8.1 Jumpstart series: http://channel9.msdn.com/series/Building-Apps-for-Windows-Phone-8-1/15#time=25m40s
In this session, Microsoft highlights that low level / raw access is possible for the following tag types through the WinRT SmartCard API:
- ISO 7816-4/APDU
- MiFare Ultralight
- MiFare Classic
- MiFare Desfire
- Felica
As the additional functionality requires the PN547 NFC chipset in the device, it only works on new Windows Phone hardware - e.g., the Nokia Lumia 830 (Lumia 930 is not supported). You can find more information about the WinRT SmartCard API here: http://msdn.microsoft.com/en-us/library/windows/apps/windows.devices.smartcards.aspx
So yes, reading MiFare Classic tags that are not NDEF formatted is possible with WP 8.1 on new hardware.