I'm the simple type...so I'd just add the treatment combination to the table as long as it doesn't exceed your budget for # of runs. If it does, well then the question is 'Which treatment combination do I eliminate?" Any way you do this you can still use the Evaluate Design Platform to compare performance measures.
But this addition of one "control" treatment combination adds another layer...since the optimal design is model driven, what does including this new treatment combination do to your ability to estimate effects? If it causes more trouble than it's worth, you may want to exclude the treatment combination from the analysis. When I worked in industry we routinely included what you called a "control" in the experiment event as a means of reassurance that some nuisance variable(s) didn't rear their ugly heads during experimental conduct or testing/measuring of responses. If the results of the "control" were close to what we expected practically, then we were more confident that the real experimental design of interest was not struck by the gremlins of chance.