You have seen it yourself many times, you log in and the pets and mounts show up first and then the characters a bit later. The gpu cant render the characters immediatly because their textures are not yet in the video ram. Of course pets and mounts are first to load as you can load them all from one location. For a character you have to go all over the place to get spicifc armor ....
That has nothing to do with GPU ram, it has to do with hard drive latency.

Throughout our experiences we've all found wow to be more CPU-reliant than the GPU. When I first started multiboxing, it was in BC with a 512MB 9600GT. It worked fine for me. Sure, textures have increased, so have other art assets, but just because he's doubled (or tripled) the relative load on his card (with 2gb of VRAM vs my previous 512MB) doesn't mean the graphics card is at fault.

Your comments regarding textures are theory in my opinion simply because they are speculation. Now if you/we had more knowledge of the nature of how textures are pulled into VRAM, at which point they are purged from VRAM, and if caching occurs for textures within VRAM(And if that caching could possibly be shared between instaces of WoW), and the relationship between the number of textures and how they are applied to the usage of VRAM, well...until then it's still SPECULATION.