iWitness: I'd say it depends on what type of rocket is used & how low the atmospheric pressure is at 200,000 feet.
Hypergolic liquid-fuelled rockets should be able to function, though whether they'd create useful thrust is open to question.
The same goes for most types of modern solid-fuel rockets.
Non-hypergolic liquid-fuelled rockets are another matter, but as they are mainly fantasy items I'd not bother too much with them.
There is a chance that Free Expansion would occur, or even that the fuel tanks would explode, if atmospheric pressure was low enough though.
Now: does anyone have solid, real-world evidence that NASA's rockets work as they claim, by 'pushing on themselves'?
You know, the phrase 'pushing on themselves' is so laughable when thought about logically that I'll use it a lot from now, until the absurdity of it sinks in...
By the same logic, I should be able to grab myself by my ear & simply lift myself up to space!
Sadly, I can't... so Zero evidence for the space-cultist's model so far eh?
Pythagoras: if you cannot work out that most 'space-rocket' launches are either completely sfx, or that the rocket trajectory reaches apogee at an altitude far too low for it to achieve orbit, then you are out of your depth here.
Go learn how these things work, then return.
Or just remove your space-horns & enter the door marked 'Freedom'...