I have heard the phrase water roots and I am thinking it refers to roots of violets started in water rather than mix?
Is there any reason that violets can't just be grown in water/pebbles if they do get roots that way?
Yes, water roots are started in water.
I grow my African violets in hydroton (clay pellets). They're thriving. If you do a search on this forum for hydroponics or hydroculture, you'll find a lot of information.
Should you decide to do it this way, dilute your AV fertilizer to about 1/10 of that is called for on the package instructions, and use it just about every time you water. I happen to use Eleanor's VF 11 plant food though. I just use the regular amount.
I use hydroton in my terrariums, I have the hydroton and a layer of chunk coir on top and the plants do well.
Do you wick?
No wicking is necessary.
The pellets will wick the water to the roots as necessary by capillary action. Check out the waterroots.com website. It's excellent.