I spent about a year running barefoot to get round constant lower leg injuries. Worked well, no lower leg injuries. Downside... lots of foot and achilles tendon trouble now and constant plantar fasciitis. If you havent gone barefoot before then I'd really advise getting some good advice first. Talk to a physio that specialises in biomechanics, get good technique and make certain you aren't trading one set of problems for another. I'd also add when I went barefoot it was at least 4 months before I was back up to my average distances, a lot of the time I had to alternate between barefoot & traditional shoes and even when back up to normal distance I struggled far more trying to extend it for event training than I did normally.
Barefoot is great in the right circumstances but a lot of its proponents dont like to acknowledge it has any downsides. It does, do your research (not suggesting you havent) and make sure you've got good reasons to risk a new set of problems against. A serious "internal" injury on the Camino is a game changer.
I just attended a lecture by a podiatrist and a physical therapist on foot injuries. They basically said that the ‘barefoot’ shoe craze has been very good for business (i.e.; created lots of plantar and ankle injuries).
barefoot as in zero rise trainers? Inov-8 terroc with added sorbothane double strike footbeds worked quite well for me. The inners were essential for the Portuguese granite cobbles. I could feel how soft tarmac was after a hundred km of cobbles.
But essentially - my advice is to use your comfiest everyday shoes.
IMHO, I would not recommend this. There are parts of the Camino, (often enough) when you are walking on rocks - not small stones, but rocks the size of your fist, or larger, which would likely be hard on your feet. I would suggest something with a Vibram sole which can take this sort of 'punishment'.