Alas, no, at this point one cannot "watch" systems form "naturally."
I personally think that such a thing would be an interesting thing to look into-- allowing stars, planets, etc to form on their own over time from dust thrown off from collisions, etc. That may also lead into star life-cycles being simulated as well, as well as more realistic collisions.
Of course, the sheer amount of processing power that would require is something that many computers lack. Perhaps, if this feature could ever be implemented, it could be something you could turn on and off? Heck, it could even be an add-on simulator or a different simulator entirely, if it is out of the capability of US at the moment.
Something to think about, I suppose.