I'm pretty sure that VLC doesn't use the graphics card to decode compressed video, just the CPU. So, your video playback ability in VLC will be determined by the CPU alone.
But I'm afraid I don't personally know how well the Mini 10's CPUs fare. I know the Atom N270 (1.6GHz) in my Mini 9 is almost capable of 720p h.264 playback. It plays simple scenes well, but struggles with fast motion.
Of course, AVI files are usually lower res than 720p and usually have simpler compression than h.264, so it doesn't take much CPU to decode them. Which bodes well for your intended use.