Given the intelligence and ruthlessness of some of the Presidents, I don't think it would resemble what it looks like today. So in that sense, no, it wouldn't. By that same token, they would make it work differently. Times have changed.
We live in the information age now, and thanks to that fact, we aren't like many of the ill informed people who weren't able to research JW doctrines. Frankly, it is scary to contemplate just how little much of the population knew about many things...
As an aside, think about this: Till Watergate, no one overtly distrusted their government. Since then, a very wide malaise has been evident towards their democracy. Information jolted people to the reality that their government was really crooked. (and it doesn't matter what party it is... We know this)
With religion, just take the pedophile explosion of the 90's. What happened? We live in the information age, and the powers that be couldn't keep the lid contained on it anymore. (its not like religious leaders started to seek sexual favors or became sexual predators in the last 40 years...)
I use those two examples to demonstrate that our times are different, and that while I think JW's could exist, it wouldn't be as it is now.... They world probably be more Mormon then anything.... But it would flourish to some extent. Maybe more, maybe less...