Yes, you will be using gravity to lower the water level. The lower end of the siphon must be below the water level and level of the upper level of the siphon. While this is normally done with tubes, it can work with cloth as well, albeit not as effectively. However, if the entire cloth/wick is not wet, then the "water" level of the end, e.g. the dry area will not be below the upper end and it will not work. With a tube, the mechanism is gravity, with a cloth, its capillary action (wetting) and gravity.
It works differently if the wick is thru the bottom of the container, but you need it to be wet if the wick goes upward and over the edge, then down. Note that the wick may wet itself thru its entire length if the material is absorbent and humidity is high (to limit evaporation), but this is not always assured. It can be tricky, however, to get this to work.
I would regard this as a long term, slow functioning mechanism. If your plants are under water, use a sponge or towel to get most of it.
You could also use air tubing sold for aquarium air pumps to siphon the water out. It's inexpensive and a "set it and forget it" way of draining a large container that you cannot move. Fill the tube with water, insert below the water level of the container (into the soil) and put the other end below the height of the container. As long as there are no air bubbles in the tubing, it will siphon water from the container, even if some dirt gets into the tube - it will just slow it down. You would need to refill the tubing with water the next time you need to drain.