No. The PS2 and PSP have fundamentally different architectures:
Some homebrew emulators attempt to run PS2 games on PSP, but performance is extremely poor—most titles are unplayable due to the PSP's limited RAM and GPU. This also requires custom firmware, which voids warranties and carries legal/ethical concerns regarding game ownership.
Best Option: Play PS2 games on a PS2, a backward-compatible PS3, or via official ports/remasters on modern platforms.