What's that phenomenon where as a child you were told a "fact", internalised it, and lived your life presuming it was true until someone points out how obviously wildly untrue it was that you momentarily question reality?
Because I was today's years old when I realised how ridiculous cutting complete blood flow would be. Thank you (genuinely!)
There's gotta be some partial decrease in circulation, though, given that my fingers on the numb hand are usually colder than my non-numb hand when this sometimes happens to me.
Maybe a bit, but there would have to be a ton of pressure. Consider the fact we have to use a tourniquet to cut blood flow typically, and those hurt like hell.
Your nerves are responsible for making your muscles move. Blood only keeps them alive, and it takes quite a while for lack of blood to actually matter. A rule for tourniquets in medicine is 4 hours if you want to keep your limb without permanent damage.
A good indicator if blood flow was actually cut off is if your limb is extremely pale (within just 1 or 2 minutes) or later goes blue. But if your nerves are unblocked, you can still move your limb for quite a while even without blood flow. Usually though, if blood is cut off, nerves also are.
I remember waking and trying to move my arm while it hung limp like a piece of meat. It was horrifying but then came crashing pins and needles after a very long minute.
Used to call asleep with arm under my head face down. Arm would be totally numb and it'd wake me up. Flip over onto my back and hit myself in the face with my giant limp noodle arm.
This can actually cause permanent damage in rare cases. Generally when you've been drinking, which is why they call it Saturday Night Palsy.
Also, as a middle aged adult, I can tell you that sleeping in the standard "arm under the pillow" position which produces this can also cause very serious degenerative shoulder damage which can result in needing one of those surgeries where you get one shot at it and there's like a 5-10% change of it failing and you living the rest of your life in constant pain.