The answer is "it depends."
Different schools manage their accounting different ways. At some well-funded schools, the limiting factor is the 11.7. At other schools, the dollars run out long before they bump up against the 11.7.
At my son's school, the baseball program has a certain amount of money for scholarships. The coach told me the number. It is not enough to fund 11.7 in-state scholarships.
But that doesn't mean he can't go after out-of state players because the athletic director manages a separate budget that dispenses what they call "in-state grants" to cover the tuition difference for out-of-state students. The baseball coach can ask the AD for these grants for particular prospects, but these funds are also limited, and he has to compete for them with coaches from other sports. Any money distributed from this fund counts as athletic grant-in-aid money, but it is "free" as far as the baseball coach is concerned, so it wouldn't affect his sense of how expensive an out-of-stater was to him. In fact, since the "in-state grant" is worth a little more than 30% of an equivalency, sometimes he can offer just the in-state grant and land an out-of-state player without spending any of his own scholarship budget.
This coach makes his offers in dollar amounts, which makes it easier for parents to figure their out-of-pocket costs, which I care about much more than what percentage scholarship my son is getting. (Unfortunately, it also puts the family on the hook for future tuition increases.)
Other schools have different situations. Some private schools know many students can get more need-based aid than baseball scholarship money, which permits them to stretch the scholarship money farther. Some state schools with lottery-funded scholarships for all in-staters, expect some of their in-state players to qualify for lottery money, thus making more baseball money available for out-of-state players.
It just depends. Every school has its own constraints and its own opportunities to stretch the budget.
One thing you can count on: there is a lot more merit money out there than baseball money, so encourage your players to take care of business in the classroom. The expected monetary value of an SAT prep course is greater than that of a similarly priced showcase.