While any trap is apart for an extended period of time, plug the drain to prevent dangerous sewer gases from entering your home. That is the purpose the water that remains in the trap when it is attached serves.
That said, S-traps are problematic because they cannot be vented properly. When water flows along a common horizontal run from another high-volume device with inadequate venting (such as the water from your washing machine, suds expelled under pressure), it will pull air behind it anywhere it can, potentially siphoning your s-trap.
It doesn't sound like the work in progress is conducive to moving drains around, so I presume you will be reusing the s-trap when you put in the new sink. The sink probably gets used more frequently than the washer, so long-term trap seal depletion is not likely a major issue. If, however, you are doing more extensive work or having any renovations done beyond the sink replacement, consider converting your drain to a p-trap with proper venting.
For now, buy a test plug and put it in the pipe coming out of the floor.
