No. PlayStation 3 games cannot run on PlayStation 2.
| Component | PS2 (2000) | PS3 (2006) |
|---|---|---|
| CPU | Emotion Engine (MIPS III, 299 MHz) | Cell Broadband Engine (1 PPE + 7 SPEs, 3.2 GHz) |
| GPU | Graphics Synthesizer (150 MHz) | RSX 'Reality Synthesizer' (550 MHz, G70-based) |
| RAM | 32 MB RDRAM + 4 MB VRAM | 256 MB XDR + 256 MB GDDR3 |
| Disc | DVD-ROM (4.7/8.5 GB) | Blu-ray (25/50 GB) + DVD |
| Architecture | MIPS, fixed-function pipeline | PowerPC/PPE+SPE, programmable shaders |
Keep a PS2 (or modded PS3/PC with PCSX2) for PS2 games. Keep a PS3 (or PC with RPCS3) for PS3 games. They don't cross.