No, it is impossible. The hardware gap is fundamental.
| Component | PS1 | PS2 |
|---|---|---|
| CPU | MIPS R3000A @ 33.8 MHz | Emotion Engine (MIPS III) @ 294 MHz |
| GPU | Custom 2D/3D (no T&L) | Graphics Synthesizer (2.4 GP/s fill) |
| RAM | 2 MB Main + 1 MB VRAM | 32 MB Main + 4 MB VRAM |
| Disc | CD-ROM (650 MB) | DVD-ROM (4.7 GB) + CD |
| Architecture | Single bus | 10-channel DMA, IOP (PS1 CPU as I/O) |
The PS1 lacks the CPU power, memory, DVD drive, and I/O architecture to even begin executing PS2 code.
PS2 plays virtually all PS1 games (via hardware IOP + software emulation). This is the intended backward compatibility direction.