According to the specs sheet for NFS Carbon, no: here is what they show and in regards to the video card, they seem specific for the chipset:
PC System Requirements
The minimum PC system requirements for Need for Speed Carbon are the following:
Operating System: Windows 2000 Service Pack 4 / Windows XP Service Pack 2
(64-bit versions are not compatible)
Processor: 1.7 GHz
Memory: 512 MB RAM
Hard Drive: 4.7 GB for CD/DVD versions / 11 GB for EA Downloader version (5GB for download, 6GB for install)
Optical Drive: 8x DVD drive (Europe) / CD drive (North America)
The Collector's Edition only comes in PC-DVD format and requires a DVD drive
Video Card: A video card with 64 MB memory and one of these chipsets is required:
NVIDIA GeForce3 / NVIDIA GeForce4 (Ti series only) / ATI Radeon 8500.
Laptop versions of these chipsets may work but are not supported
Sound Card: DirectX 9.0c compatible
DirectX: Version 9.0c
Online Multiplayer: 512 Kbps connection; 2-8 Players
Input: Keyboard, Mouse
Optional: USB Steering Wheel / Dual Analogue Gamepad
Of course these are listed as minimum specs, so the card might work, but he FX2500M series is a workstation video card designed for use with graphical design programs and such.