Disclaimer: I'm not a linguist, and I don't even talk like one on community radio.
When answering this question, it's important to consider why languages change, just as much as why they don't.
Restatement of the hypothesis
First, let's take a more detailed look at your hypothesis: increased language education $\to$ decreased language change. Basic $P \to Q$ hypothesis, right? (I.e., if $P$ is true, then $Q$ will also be true.)
I believe your (unstated) syllogism relies on these assumptions:
- All people who study language make fewer mistakes
- Language change occurs because people make mistakes or because enlightened people choose to change the language (e.g., to simplify it, to introduce new terms, "jokes", etc.).
And the syllogism is if more people study language, fewer changes will occur.
The logic itself holds true provided the assumptions are true. So let's look at those:
1. All people who study language make fewer mistakes
This does seem like common sense. Someone who has limited literacy will be more encouraged to converse based on what they hear. Although language (especially English!) is notoriously irregular, there are enough patterns that a more educated person is likely to get the subtle rules right more often than a less educated person. Without a lot more research and math, I'll let you have this assumption, at least on a stochastic basis, but keep reading, because it's more complicated.
2. Language change occurs because either:
a. People make mistakes
b. Educated people deliberately change the language to simplify it, etc.
This is where I think you'll find the question is much less clear cut.
My personal feeling is that the effect (in isolation) from 2(a) $\ll$ 2(b). To quote an actual linguist on this one:
All language is a popularity contest. — Erin McKean 
Sometimes there are mistakes (or "happy accidents", if you prefer) that people make with language, that are either perceived to be clever, or funny, so people repeat them.
If I come up with a funny new word and tell it to my wife, and she tells it to a few people, it will have a certain network reach (and probably be forgotten long before it hits a hundred people). If a major celebrity does the same thing on Twitter or YouTube, hundreds of thousands of people will be using the word within days. If more people continue to spread it, it has a real chance of becoming a lasting addition to the language.
It is very hard (and, usually, very harmful!) to study language in isolation. Even though I only speak my born native language, I am frequently affected by other languages.
For example, my Czech friend speaks excellent English, but occasionally phrases things differently, or chooses different words than I would. The important thing, here, is that her English is irrefutably correct. She never violates any grammatical rules or chooses words that do not fit the intended definition. In other words, her idiomatic usage differs from mine, but neither one of us is "wrong". I very much enjoy these differences.
Going beyond that, foreign language loanwords still regularly make their way into common use. In fact, even though English originates primarily from North Germanic origins, we still keep adopting new (modern) German words today, such as "blitz", from the German "blitzkrieg".
The other side of the coin
There's another side to the coin: language affects people. I'd suggest looking into linguistic anthropology for more information on this topic.
There's therefore a symbiotic relationship between Language $\leftrightarrow$ Society.
Language is a living thing.
Languages evolve because they're used by people, who are shaped by those very same languages. If I invent the word blersnogga and use it in a way that makes you giggle, you've been affected. And when you're affected, you're more likely to want to use that word to affect others. Good education isn't required to use language in a way that affects people (Mark Twain is a famous example of that, having left school after fifth grade, although he did self-educate later).
Edit based on comments
Specific to your question (clarified by your comment on "whether changes would slow, or stay the same"): my assessment would be:
- Yes, education would have an effect on how a language changes
- However, that effect would be comparatively small and very hard to isolate. (We are after all looking at how the overall language evolves, not just how a few people speak it.)
- The rate at which language changes might slow, or it might even speed up. Let's say everyone was perfectly literate in their language, and had a higher average vocabulary (comes with higher literacy) than a similar less-literate population. Who do you think would make up more words and other changes? Who would be more likely (and more successful) to propagate these changes to others?
What I'm saying is, language change cannot happen in isolation, so the best answer I can give you is, "it depends, but the effect of education is probably not very big, compared to the other effects discussed in my answer". I realize this is about as hand-wavy as it gets, but hopefully I've at least helped identify some of the variables in the equation.
Language is a living thing.