I saw it at Home Depot. They had a demo display utilizing the pump unit and a laundry sink, in the Plumbing department. Looked like the pump unit was sitting next to the sink, on the floor, so I guess there was no need for it to be directly under it. This would mean that it could, in theory anyway, sit on the floor next to the washer. Ask the pluming assistant there.
I believe the basic design consists of a holding tank, a pump, and some activation trigger to turn on the pump when the tank is full. The question is whether the pump unit can pump out the water at least as fast as the washer would pump it in. Otherwise, the holding tank would overflow. Ideally, the capacity of the auxiliary pump should be larger than the washer’s pump.
As an alternative, you could install (if you don’t already have one) a laundry sink, allowing the washer to pump into the sink instead of the drain. Laundry sinks usually have the capacity to hold more water than a full-load washer does. In that way, the laundry sink acts as the holding tank, and the auxiliary pump can take its time discharging the water.
Good luck, and let us know if you have any more questions, and how it turns out.