I've been using an EyeFi card in my 5D3 for the past few weeks. I've found the EyeFi to be... flaky. But in its defense, it's a refurb I got from woot.com.
The way I've been doing that is to do RAW only in the simultaneously-record-to-both cards mode. When I have a shot I want to transfer, I run it through the in-camera JPEG processing, and it transfers to my iPhone using the built-into-the-card ad-hoc network. Works reasonably well most of the time, and I have a 32G CompactFlash for more stable storage.
You can't use an EyeFi in a Canon with a CF adapter. I tried it with all of my Canon bodies that use CF (XTi, 40D, 5D Classic) and it just flat out refused to recognize the card as a viable storage medium. Worked in my Nikon D70, more or less, but no go with the Canon. Googling it reveals that everyone else who's tried it agrees. Just don't bother--either get a Canon that supports SD, or give up on the dream of EyeFi.