Anything is possible, but is it worth the effort? USB is a high speed differential analogue interface, it is possible to get a Serial interface engine IC to convert this to digital, but then you have the protocol to sort out, bit stuffing, clock synchronization, packet recovery, handshaking and all that. It is a lot less headache to use a pic chip with a USB port on it such as the 16C765. Only supports low speed usb though. Or use a chip like the philips PDIUSBD11/12 as the usb interface.
Microchip have been threatening to bring out a full speed version for some time, still a future product though. If it was easy, they would have it on the market by now.