I fail to see what the point of that would be. Any vassal not in a faction is by default a loyalist - because he sends troops to the liege under the general mechanics if the liege goes to war with one or more factions.
By definition, this is obviously correct. But I still think it would make sense for "active" loyalists to receive a positive relationship modifier if they engaged rebels with their own levies. Wouldn't have to be guaranteed, though. Maybe the king just tells them "I didn't ask you to help me." afterwards ...