Here's a link to the official Blizzard World of Warcraft site with video cards that are supported by Blizzard for World of Warcraft.
As you can see ATI Radeon 9xxx series chips are indeed supported by the game, to be absolutely sure you should compare your computer to the game's requirements;
Minimum system requirements for World of Warcraft:
Your computer will need a 56K or higher Internet connection
You must have a valid e-mail address
Windows® System/OS (ME, 2000, XP):
Intel Pentium III or AMD Athlon 800 Mhz or higher CPU
512 Megabytes (MB) or more of RAM
32MB 3D Graphics card with Hardware Transform and Lighting (such as an Nvidia GeForce 2 class or better)
6 Gigabytes or more of available hard drive space
4x CD-ROM drive
DirectX® 9.0c (included with game) and latest video card drivers
Mac® System/OS:
933 MHz or higher G4, G5, or Intel processor
512 Megabytes RAM or higher
ATI or NVIDIA video hardware with 32 MB VRAM or more
6 Gigabytes or more of available hard drive space
4x CD-ROM drive
MacOS X 10.3.9
Recommended system specifications for World of Warcraft:
Broadband Internet connection
Windows® System/OS (ME, 2000, XP):
Intel Pentium IV 1.5GHz or AMD XP 1500+
1024 Megabytes (MB) of RAM
64MB 3D Graphics card with Hardware Transform and Lighting (such as an Nvidia GeForce FX 5700 class or better)
Two-button scroll-wheel mouse
Mac® System/OS:
1024 Megabytes (MB) of RAM or higher (DDR RAM recommended)
ATI or NVIDIA video hardware with 64 MB VRAM or more
MacOS X 10.3.9 or newer
If you are running below any of these requirements, then you may encounter graphical issues, crashes, or slow down which Blizzard will be unable to address or troubleshoot.
Note: Due to potential programming changes, the Minimum System Requirements for World of Warcraft may change over time.
