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If PC modem card is on PCI, well that's an overkill aplication for PIC micro.
If it's on ISA, it could work but you still need to provide the drivers for the chipset included on ISA board. If it's just for fun it's a chalenge for you to try. But if you intended something for mass production, my advice is to try an embedded modem. I know it's not cheap as modem card, but you can't find forever ISA boards, which are obsolete.
You can find embedded modem on manufacturers like:
**broken link removed**
**broken link removed** Connexant shape compatible
You'll have full support for AT commands through serial interface.