I'm not a Designer customer, but I imagine you could query the type of license in use by the client?
Unfortunately, that will not tell you if a user has started a DE workflow session. Only that the user has checked out a DE license. The license is checked out as soon as ArcMap opens. There must be some way to tell because the save and close design buttons only light up when you are in a session. You could assume that if the user is editing and the version name starts with ‘WN’ and contains ‘_DN’ that they are in a session. However, there must be a better way than this.