temprory set up of a gravity works print washer

I want to set up a Gravity Works 11x14 print enlarger on a rolling cart in a guest bathroom that I can roll in and out.

My question is can it be done?

1) Does the print washer have to be in the sink to prevent overflow or can the flow be adjusted so the hoses can be left in the sink with little to no chance of a leak?

2) Does the print washer have to be in the sink or shower fully to drain at the end of the wash session or are there drain hoses that can be draped over the sink to drain the washer completely.

2) How high does the cart need to be in relation to the height of the bathroom sink for this to work effectively. Can the height of the cart be a few inches below the sink countertop level?

My original set up with a 16x20 GW washer was on a stand which I built from 2x2's, standing next to the tub, but the bottom of the tank was higher than the tub edge. The hoses will drain into the tub fine with this setup, but if I was to advise someone else, I would say if you could put the tank in a tray (like a 16x20), you'd be safer.
My tanks actually sit on the counter next to the darkroom sink, and drain into it, never a problem in 18 years.
If the bottom of the tank is below the sink, or tub, or whatever, the bottom drain hose will have to rise up over the sink to go into it, and I don't know how well this will work, but it doesn't strike me as a good idea. At some point there won't be enough gravity pull to drain it (like maybe when the water level in the tank is at the highest level of the drain hose.)
I would just make the cart high enough to clear the edge of the sink. Also, when you stop feeding water, disconnect the feed hose from the source, and place it in the sink. The tank will drain almost, but not completely from this hose and the normal drain hose. My tank is almost never totally dry.
Just be sure if there are kids around that you keep an eye on things.

Why not put a temporary shelf across the edges of the tub & move the washer when it's empty?

Thanks for the responses. The bathroom I use is "untouchable" regarding modifications as it is a guest bathroom with new fixtures. As such, I just bought a Dalite projection cart which I don't need to assemble the top shelf. If I place the print washer (which is on the low Dalite platform) next to the shower threshold, the drain hoses will just drape over into the shower. The sink faucet will be the source of water. I can still use the shower head to rinse and for a water source. This set-up will be the least offensive to my wife in maintaining the pristine look of the bathroom.

If you are pre-treating

Lawrence Chai said:

Thanks for the responses. The bathroom I use is "untouchable" regarding modifications as it is a guest bathroom with new fixtures. As such, I just bought a Dalite projection cart which I don't need to assemble the top shelf. If I place the print washer (which is on the low Dalite platform) next to the shower threshold, the drain hoses will just drape over into the shower. The sink faucet will be the source of water. I can still use the shower head to rinse and for a water source. This set-up will be the least offensive to my wife in maintaining the pristine look of the bathroom.

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your prints with Perma-Wash or other hypo-clearing agent be aware that this water is very corrosive to chrome (and other finishes) which is probably in abundance in a modern "pristine" bathroom with new fixtures. I made that mistake in a kitchen where I ruined a garbage disposal and the finish on a dishwasher door in addition to the drains and faucet chrome using the area to wash fibre-based prints in an 11x14 printwasher.

I think you have a clear case for "the Boss" to allow you to build a dedicated darkroom far away from her "pristine territory".