This is embarrasing to ask -- as I know Linux will run pretty damn well on most setups... but I have to ask for my own sake... please bear with me.
I'm installing (or planning to) Mint on one of those Mini-ITX systems. The goal was to create a basic music server with as few moving parts as possible (heat sinks instead of fans, low-powered processing, etc.) I searched the forums but couldn't find much -- so, a simple yes (things will work) or no (you're screwed go to a lighter weight linux distro.) Bear in mind, my 18 month old is watching me type this, so if you say no, you're hurting the baby.
Motherboard: VIA C7 EX10000EG
-VIA CX700M2 Chipset
-Integrated VIA UniChrome PRO 2