I was wondering what effect placing quad channels between the feet on the base of the board will have on it's characteristics - any idea on how it will affect the ride and what will be the overall effect of them?

You see single concave all the time and sometimes a double but very rarely a quad aside from on a wakeboard.

Thoughts?

Channels give more area for the same width , and more directional drive and direct the water under the board giving lift.

Don't know how they would work on a TT. They have worked fine on surfboards for years but are less popular cos of the time and expense of shaping and glassing vs concaves which basically do the same thing, however concaves take out rocker down the center line, where as channels generally don't.

Sorry my mistake I whould have called them concaves - not channels.

Essentially what effect will a quad concave between the feet have on a kiteboard - any ideas or experiences? How would they compare to a single concave?

When edging, water rarely flows parallel to the centerline of the board, so multiple concaves or channels that run parallel to the boards center line have little effect. Double concaves however form a ridge along the center line which if shped sharp enough might release some water and avoid a little friction (negligible). Single concaves have the effect of taking out rocker thus making the board a little faster. It should be noted however that rocker on a kiteboard is a compound of bottom curvature and flex pattern. Should yu have a soft (flexy) board with very little rocker, you may end up with a slow board, regardless of the concave.
When riden flat, concaves do contribute some directional stability and act as a damper for high frequency vibrations (caused by small ripples). But this effect can be achieved as well with propper fin placement and selection as well as with material choice and flex pattern. Adecuate pad selection might take care of the vibrations as well.

IMHO from board builder perspective concave adds stiffnes to a board, thus you have to use less material to get the same result.