In fact the commercial PS1 emulator SONY bought before making the PS2 had a "pseudo" bios which used a sort of HLE concept. I don't recall the emulator name though.
Oh and I believe the bios contained on this emulator is slightly changed to ease the task of HDD access. Just like the PS1 bios on the PSP system software, which is modified to simplify the emulator.
SCPH-10000_GH-001 SCPH-15000_GH-003 SCPH-18000_GH-008 SCPH-30001_GH-005 SCPH-30000_GH-016(V4) SCPH-30001_GH-010(V4)
2xSCPH-10190, 2xSCPH-10350, 2xSCPH-10280
"**** j0 hackers!"
-Sjeep (As seen on TOXIC OS ELF...)