Count me among the many who like doing a few 200s at the end of a tempo or threshold workout. I will ask my kids do them at 1600 pace. They will usually run them closer to 800 pace, which is fine, as long as they aren't straining.
As far as the volume, a 6-mile tempo and 6x200 are both on the high side unless you are a very high-mileage (or very fit) runner, IMO. I think of that as training for 8K or 10K racing, or college XC, perhaps. For my high school kids, 20-25 minutes of tempo or threshold work tends to be my upper limit, with 3-4 x 200 or strides.
So, while your workout isn't egregious, it's hard enough that I wouldn't hesitate to let your coach know if it feels like too much. He may disagree, but it's healthy to have open communication about things like that. Just be very respectful and be prepared to defer to his opinion. Most coaches want to know when their runners are feeling overloaded.