See
pSX Author's latest post on Playstation 2 emulation in pSX. Stop dribbling!
As yet, pSX will run a PS2 BIOS, and there is apparently one game working (and someone else has claimed another), although we don't know which one - pSX Author's screenshots are with a WIP he's built. However, you'll need a fairly high end machine and the CPU must have an SSE2 instruction set.
Hopefully, though, given pSX Author's track record, when it does happen, Playstation 2 games on pSX should require significantly less resources than they'd require for PCSX2.