If the appropriate size of pipe is used, you should have no issue with a single mop sink tied into your washing machine's drain. The average drainpipe size for washing machines is 2 inches, which is also what is used for showers, kitchen sinks and other areas in the home. Anything smaller than that will not sustain two drains at once.
Just as important as the size of the pipe is the venting for the pipe. Without proper ventilation your pipes won’t drain properly. Instead, they will "glug," similar to how a water bottle will spurt and gurgle when it is upended and drained all at once. Your drainpipes need to have proper ventilation to ensure that the flow of water is smooth.
Plumbing is a fairly straightforward process in that it basically involves sticking pipes together, but there are a few things to keep in mind. One of those is that nothing should be allowed to block the pipes. Not only does the ventilation pipe need to be free of debris, but the drainpipes from the washer to the mop sink need to be clear of buildup, such as pet hair or food particles, to facilitate drainage. If the pipes aren’t draining properly, you will notice water draining slowly or not at all from the mop sink or excess water coming out of the mop sink when the washer drains.
As long as you are only tying in one mop sink to the drainpipe for your washer, you shouldn’t have any issues. However, the more branches you have, the more problems that can crop up. You also need to have sufficient slope for the pipes to drain: no less than a 1/4-inch in every linear foot of slope. Local plumbing codes will have variations on federal codes so consult with a local plumber.