If this is a single pahse service, no problem (as long as the appliances are rated to handle 208- a 240v rated appliance might have problems)
IF you are talking about a three-phase system, with a 208v "wild" or "stinger" leg, you have a problem.
The three phase panel in this case is not listed for use as a "lighting and appliance' panel, only as a 'power' panel. I just had an experience with someone who didn't appreciate this, and had some receptacles supplying 208v! What you must do is use two of the 120v legs to serve a separate single phase panel, and draw your circuits from there.