The use of both a starter and commercial yeast is quite common. Jeff Varasano has described doing this, and I recall speaking with a baker at the Sullivan Street Bakery in NYC who told me that they used some commercial yeast along with their natural starter. I believe that it was a belt-and-suspenders type of thing to get more lift in the dough, or in case the natural starter didn't work as intended.
It's been a long time since I have used natural starters, either alone or with commercial yeast, but my recollection is that the doughs I made that had both forms of yeast produced finished crusts in which I could not detect the presence of the starter. However, we do have some members, like Chau, whom I believe uses both forms of yeast concurrently and who may be able to comment on their results. In your case, if you are using a full cup of starter material and that amount represents a large percent of the formula flour (e.g., around 30-40%), and if your starter is in good shape, you may not need any commercial yeast. According to Ed Wood, in his book, Classic Sourdoughs, one cup of starter culture weighs around 9 ounces. If you are using the original recipe that Tin Roof referenced, with 26 ounces of flour, the cup of starter culture would be about 35% of the total formula flour. If my memory is correct, that would be about the amount that Nancy Silverton recommends to make a basic country white bread in her book Breads from the La Brea Bakery (page 40). Having made that bread, with no commercial yeast, I can tell you that if your starter is in the proper condition, you should get a highly detectable sourdough flavor in the finished crust. However, that flavor is likely to be far more pronounced than a crust made using a much smaller amount of starter and a different fermentation protocol.
Sometimes you just have to conduct experiments to see what you get. Those experiments will be your best teacher.