Mono-Systems, Inc. 1-1/2-in x 60-in Low-Voltage White Cord Cover Model CH-12, can it be removed from wall without taking paint with it?

I used small sheet rock screws...can "easily" be patched should you need to take it down.

Yes, it will usually damage the painted finish on drywall. If you care to try to heat the surface a little (perhaps with a hair dryer) to soften the adhesive, and slooooowly lift the channel up starting from one end, it might work for strong painted finishes such as well cured high gloss paints; no guarantees though. I'd suggest trying it in an inconspicuous area first.

Don't count on a clean removal from drywall. Some enamel paints on wood will release the bond.