Can I run two ATI Radeon HD 3870 X2 graphics cards together in Crossfire, or will this not work due to the dual GPUs (X2)?
Yes, you can use Crossfire. See here:
In general, yes, all dual-GPU ATI cards can be run in a Crossfire config for four effective GPUs. The maximum number of GPUs in crossfire is four.
There are not a lot of dual-GPU cards to choose from though, and the ones out there are expensive.
(it is also possible and supported to use three or four single GPU cards on one motherboard, if you can find a mobo that has the right number of video card capable PCI express slots!)
Any four-GPU config would also require a truly massive power supply and extremely good cooling, so be careful. This is the one instance where all those ridiculously over-specced gamer rigs are actually justified!