No it absolutely does not rise like it does with an AAS cycle. That's why sarms can be so good to run between cycles. You will still get some rise from your myostatin but it won't go too far above your baseline. The more anabolic of the compound and the strength of it, will rise myostatin the quickest, so steroids do this to a very large degree....especially things like Tren, and many orals. However all steroids will make it rise to peak over time.
Sarms don't have the same effect at all. That's why people continue to make gains throughout a sarms cycle, until they start desensitizing to the compound....not because of myostatin