An Omnibus hearing is a status confernece hearing. One may continue the case, set it for plea (or perhaps plea that day), or set the matter for motions/trial. This is a hearing where you let the court know where the case stands as far as preparedness for trial, or the status of negotiations. In King County, the court has required defendants to be present. If the defendant is not present, chances are high that a warrant will be issued.
In general, a defendant must be present at every hearing for a criminal charge. The only way this can change is if a judge excuses the defendant in advance. If a judge has not excused the defendant's presence, the person must appear. If he or she does not show up, the judge will likely issue a warrant for the person's arrest.