Jeffrey, presses used to be part of GS as well. They contested a one arm press for reps, under the same rules as the snatch- max reps, one hand switch. It was dropped for the same reason that the Olympic press was dropped- judging difficulties. Now that it is not contested, few GS coaches prescribe it.
It stands to reason that being stronger in a movement like the press would improve the jerk and snatch, and that training the press would be beneficial. In the early 90's, several Russian sports scientists formulated strength standards for GS. However, Rudnev and Lopatin did a study and wrote an article about this. Lopatin was a world champion in GS, and fell well below the published strength standards. The only area in which he exceed the standard was running. The published standard called for "Junior ranking", and Lopatin qualified with "Adult ranking" (if these terms were defined in the article, I missed it). The article is at:
http://www.iksfa.com/drupal/index.php?q=node/58
Some nuggets to give you the gist of their findings:
"Thus, strength endurance is not a determining factor in Kettlebell Sport lifting. It only allows you to perform at fast tempo for 1-3 minutes. For Kettlebell Sport lifting is required endurance which allow to perform 10 minutes of competition time.. Therefore, we should talk about the special endurance, which is necessary to work with pauses between repetitions sufficient for recovery to the next repetition (tempo of snatch, jerk)) (Lopatin, 2000; Romashin, 1991). Exceeding the optimum tempo for the athlete and is the main cause of fatigue and premature termination of the 10-minutes set, rather than lack of development of strength endurance, mental strength or motivation, as noted in their studies Vinogradov (1998). "
"Thus, the importance of strength component to produce force output In Kettlebell Sport lifting is not determinative, as indicated by most researchers. Localization of muscle strength of Kettlebell Sport lifter is defined by distribution of slow and fast twitch fibers which means that the development of strength required a level not exceeding 70% of maximum voluntary force (MVF) (Platonov, 1997). "
In short, they determined that strength (such as presses and squats) only benefit the lifter in GS up to a point, and that that threshold is pretty low. They credit special endurance (i.e., cardiovascular endurance, grip endurance, etc.), recovery ability, and pacing as determinative factors in GS success. The world champion in his weight class could not meet the proposed strength standards, but exceeded the cardiovascular endurance standards.
Your question was about grinds as a useful supplement to ballistics. The article's answer would be that once an athlete is strong enough, grinding strength no longer adds reps to high rep ballistic lifting.