if it can run dolphin, it can run pso.
i found this online but it looks very old.
Here are the Phantasy Star Online: Blue Burst System Requirements (Minimum)
CPU: Pentium III or Athlon equivalent
CPU SPEED: 700 MHz
RAM: 256 MB
OS: Windows 98SE / Me / 2000 / XP
VIDEO CARD: Direct3D compatible, 3D graphics board, minimum 32 MB VRAM (NVIDIA GeForce3+ / ATI Radeon 8500+)
TOTAL VIDEO RAM: 32 MB
3D: Yes
HARDWARE T&L: Yes
PIXEL SHADER: 1.1
VERTEX SHADER: 1.0
DIRECTX VERSION: 9.0b
SOUND CARD: Yes
Phantasy Star Online: Blue Burst Recommended Requirements
CPU: Pentium 4 or Athlon XP
CPU SPEED: 1.4 GHz
RAM: 512 MB
OS: Windows XP
VIDEO CARD: Direct3D compatible, 3D graphics board, minimum 64 MB VRAM (NVIDIA GeForce FX / ATI Radeon 9600+)
TOTAL VIDEO RAM: 64 MB
3D: Yes
HARDWARE T&L: Yes
PIXEL SHADER: 2.0
VERTEX SHADER: 2.0
DIRECTX VERSION: 9.0b
SOUND CARD: Yes