is it possible to run a 4k display using an eGPU on a mid 2012 MacBook Pro (non retina)
Well, i guess you solved your problem by now, but I still wanted to answer, since I recently looked into eGPU options myself. 

If your sole aim is to run a 4K monitor (and your GPU doesn't support it), you could probably also get a USB graphics adapter. You find a selection here. This certainly is a much cheaper option, but probably too slow to watch videos, etc.

If you are into some more horsepower and want to place a powerful GPU into your Sonnet case, I suggest you take a look at the TechInferno forum. There is a growing community building their own eGPU solutions. If you look at their table with implemented projects, you will also find a number of solutions that used the Sonnet housing.

However, be warned. It is more complicated than just placing a graphics card into your PCIe case. Usually these cases do not provide enough power to run a GPU, and you will have to provide an additional power supply. Since this is all non-standard solutions, you may even have to solder on rather expensive hardware. So proceed at your own risk...