I don't see why would it be impossible, but it certainly wouldn't be practical.
Why do you want to do it? Do you want to compile a C++ program in flash? You could call g++ from a flash application I guess.
Also a flash mmo would NOT be a good idea. actionscript is a bit to specialized for that kind of work. Flash games are fine and all, but i just dont see it playing out well on a massive level.
If you want your MMO to be web based, pick up java, it's syntax is C like, so it wont be a HUGE step away from c++, and then if you really want to work with c++ on it, you can always write that interpreter in java (which would end up being a lot easier than doing it in actionscript :P)
ALL in ALL, forgo the flash unless it's absolutely required.
You could always write a command line interpreter for c++ in flash
Nice joke.
You could call g++ from a flash application I guess.
You can't. You are simply not allowed to by the Flash runtime. You could do that from Java, providing the user accepts it. But still the idea is crazy. C++ can't do that, simply. Java is an overkill (you won't be solving differential equations, will you?). Flash is IMHO good for the client side MMO. See this: http://witcher-versus.gamigo.com/. Done in Flash.
Yea, that's not an MMO. It's an online game, and it's multiplayer, but it's not an MMO. I dont expect you to know that though, you dont come across as the hard core MMO gamer type.
EDIT: no thats not an insult. Sorry it looked a little brash.