The CPU isn't emulated - they're both MIPS architectures, with the PSP's processor instruction set being a superset of that supported by the PSX.
I don't know much about the popstation 'emulator', but I would expect a compatibility layer for mid-level graphics and sound calls. This isn't really 'emulation' - it's more a matter of providing an API that fulfils the same contracts as the original hardware. Naturally, undocumented behaviour or quirks might not supported, which may explain why certain games are hard to port.
There wouldn't really be much 'extra' processing required to intercept the hardware calls. Yes, the requests would be deferred through an abstraction layer, or some kind of memory sandbox mapping for low-level operations, but you shouldn't be doing anything _that_ 'intensive'.
And remember, even recompiling assembler can be performant if you cache generated procedures and do smart optimization / branch prediction etc. Just look at the JVM - Java applications are essentially "compiled" to a generic assembler for an 'idealized' processor architecture, then reinterpreted on the fly via the virtual machine. Java 1.0's naive implementation was pretty slow, but since hotspot speed has been mostly a non-issue.