Can you use an external PCI expansion box for mining? I'm wondering if plugging cards into something this external pci expansion box would be effective in a mining setup. 

I guess it depends on how much bandwidth is used, but I don't know how bandwidth intensive the mining process is. Has anyone here used a setup like this for mining?
The amount of bandwidth used for mining is absolutely trivial, so bandwidth won't hurt you much here. Of course you would have to use something like this box because this one doesn't appear to be nearly deep enough for a full-length video card. Using the backplane from this box in a custom enclosure might be worthwhile.

The secondary problem you'll run into is power. This unit appears to have just enough power supply to power the communications between ports. An additional PSU will be needed for the GPUs themselves which, conveniently, typically draw most of their power from four or six pin connectors.

So in short, using this backplane in a separate enclosure with an external power supply (and a lot more airflow) seems pretty viable to me. Of course I haven't personally done this so I make no guarantees, but if someone has actually attempted this I'd love to hear about it.