The data imprinting will, absolutely - it fogs non-IR film to the point that I can even read letters and numbers, and it ought to do the same to IR... ;-)
I'd be more concerned about IR fogging thanks to the film start detection/barcode reader, which uses a IR diode. But I have no idea whether that actually is in action after finding the film start adhesive strip. And many IR diodes emit wavelengths way outside the sensitivity of the current crop of IR films (which don't extend much beyond visible). But I haven't tried it yet - the AF can't adjust for IR and manual focusing is a mess, so that it would hardly be my primary choice for an IR camera.