short answer: No, not usually.

long answer: It's important to remember that even though there are these "governing bodies", perhaps most famously L'Académie française and Real Academia Española, they don't actually hold power over people's speech. There was some recent news about the Swedish Academy updating their dictionaries and a lot of people (on Reddit) were upset because they saw it as the government saying certain slang words were now encouraged, but that's not actually the case.

The Academies, generally speaking, have two functions:

1. Document the language, to include changes in usage or new vocabularies. This is particularly useful when a country (Republican China in the 1930s being a great example) needs to standardise terminology for things like the STEM fields, when before that point everyone's kinda using their own translation of foreign terms, if not just the foreign terms as they were in the original language.

2. Determine and maintain the standard form of the prestige dialect, the form used for academic publication, passing of laws, official documents and the like. This is what we refer to as a register. How you speak with your friends out drinking at the bar is another register. How you talk to your elderly grandmother is another register. When you're writing an essay to get into college, it's not that they're testing how "correct" your use of the language is (even though that's what they themselves might think they're doing) but rather they're checking your ability to use that register effectively. For some people, switching registers is actually not something they have much experience with.

However when it comes to natural speech, these Academies have little influence, and the language continues to change. The extreme case would be that the Academy-dictated register stays the same for so long that people stop associating it with the thing they're speaking. However that mostly doesn't happen because the people running these Academies have some sense and they do adjust to changes in usage when they become more widespread.

Languages change. There are some things that accelerate or reduce change. For example languages in contact with other languages will change a bit quicker regarding certain features. We see this tied to wars and historical migrations, not just in the sense of one group conquering another, but also in peaceful migrations where aspects of one language have been adopted by another, or where two languages with two different complex ways of handling the same function tend to merge resulting in a much simpler single way of doing that. I can give you specific examples from history but it's all going to be in East Asia, so let me know if you're interested.

Additionally, languages/varieties with fewer speakers have greater potential for change if there's nothing unifying them (mass media for example) because the naturally occurring changes can pass through the group more easily. You see this in places like Albania which is tiny but had huge diversity of dialects simply because for a very long time people stayed in and around their villages, effectively isolated, and without pressure from other dialects to maintain some conformity.

The way you could argue that the Academies, or lets even just say "standard dialects" slow things down is really if you only look at the group of speakers who are well off and in power. However even then it's largely not really there but is just their perception. As a loose rule in sociolinguistics: everyone thinks their dialect matches the standard, even when it verifiably doesn't.

Hope that helps. Let me know if I can expand on anything.