They will absolutely separate you from your bag if you get bumped. While they might prefer to bump folks without checked luggage, if they need your seat, they'll buy you off the flight and let your bag launch without you.

As Spiff said, positive bag match is a myth (on domestic flights at least, though I once had my bag make it onto a DFW-FRA flight that I didn't make), and has been since the implementation of 100% screening of checked luggage.