ORAC|: possibly. I did see a comment on the original parabolic arc thread that suggested liquid oxygen would be used to cool the compressor. Sounds extremely iffy to me! I believe that the SABRE engine cools the air through the pre-cooler assembly and the air then arrives at the compressor. I suppose alternatives could include contact cooling directly at the first stage of the compressor and believe such compressor cooling has been used in conventional jet engine designs for subsonic increases in thrust at various stages of flight.
This article (which you have probably seen) talks about the possibility of putting a pre-cooler onto an EJ-200, but I haven't heard anything more about that..