No. The Sims 2: Pets for PSP is a stripped-down, pet-focused spin-off. It does not include romance, marriage, or "girlfriend/boyfriend" mechanics found in the PC/console versions of The Sims 2.
Developed by a different studio (Maxis → EA Redwood Shores / later Griptonite), optimized for UMD load times and limited RAM. Focus shifted entirely to pet simulation.
For the full Sims 2 experience with relationships, play on PC (Ultimate Collection), PS2/GameCube/Xbox, or Nintendo DS.