As long as the effort parameters are correct, your 20 x 200m workout should be a staple session for 800m runners everywhere.
To get the effort parameters correct, try the workout with the 200m reps run at about 2 seconds slower than your current mile race pace. This will likely seem too slow to be challenging, so you can increase the speeds to your mile race pace in the middle of the session. The effort by the middle of the workout should involve hyperventilation and a slight laboring feeling (maybe a little onset of "burn") during the last 30-50 meters of each rep, but should not involve actually tying up. Aim to run at least 15 reps and possibly 20. You are finished when you cannot continue the speed on the 200m segments without tying up, so try to work your way down after about 5 opening reps toward the speed that you think you can handle for 15 more reps.
The recovery should be jogged. Staying active during the recovery interval ensures that the muscles do not tighten and that your blood does not pool (you should stay above 65% of your HRR for this). Ever-increasing quantities of lactate produced during the session are better processed as fuel or reconverted to pyruvate in the heart if the circulatory system remains active and the muscles stay in motion.
If you were to use Veronique Billat's criteria, you would be jogging 100m between each of the 200m reps in the same time it took to run the 200m. But you are to become an athlete who is not restricted by external criteria; rather, you will know your body and you will know the purpose of the session. You will therefore begin with some reasonable guidelines but will learn to find the correct recovery pace and duration by intuition. You will also avoid asking yourself, "What could I run for race distance X based on workout Y?" This is not an indicator session, so it doesn't matter how fast it is, only that you got the correct training. You should improve your times for this session as you get fitter during the season, but you should not force the workout just so you can have a better average in your logbook and convince yourself you're faster. Therefore, do not repeat this session every week. Wait until your fitness and sharpness improves to the point that the times on this will be faster without your having to try any harder than before.
Once you learn and apply the correct methodology, you will discover that you do not require a lot of training at faster than race speeds.