It depends on whether you meant an America with lots of practicing Catholics or an America being controlled by Catholics in government.
The first, well, judging by this forum, things could get a bit scrupulous, among other things, but if charity prevails there are worse problems to have.
The second give me pause, for many, many reasons. If a few people manage to establish an oligarchy in a democracy, even for the best of reason, the long-term results are usually not pretty.
Although we have a duty to vote and add a sane perspective to the civic discourse and some of us have a vocation to serve in government, our main job to change hearts, one at a time, by the exercise of love. We must look back into our history and remember the pitfalls in putting power before service.
This is not something we need to dream about. We have our work to do, and can trust that God will accomplish what He has set out to do. While something tells me that taking over the government isn’t in those cards, I would not have a problem with it if the Church was able to keep the main thing the main thing. In a situation such as you describe, that could become our main work.
In other words, we would still have much work to do. That much isn’t going to change.