FSU cameras are based on the pre-M design of Leicas, which had a rotating shutter speed dial. You could change the speeds on those older Leicas before cocking the shutter, but you didn't know where the shutter speed was set because the dial is in a different direction before you wind the shutter.
On some FSU cameras -- their Kiev 88 imitation hasselblad is a prime example, but i've seen it said of their contax copies as well -- failing ti wind the camera before setting the shutter speed can cause actual damage -- although since most Kiev 88s came from the factory pre-broken, this is a fine distinction.
An M3's shutter speed can be set any time. Spaces between the set speeds also work, although only as an approximation and not between 1/30 and 1/60 (or 1/25 and 1/50, depending on the age of your camera) because that is where the camera shifts over to the slow speed gear train.
A good way to test the condition of your camera is to set it on 1/15th of a second and fire the shutter while listening closely. You should hear the gear train buzz as it holds back the second curtain, followed by a sound best described as a bb bouncing on a table -- that is the retard bouncing back after releasing the second curtain. If the sound is nice and crisp, your camera's slow speed train is in good order.