It wouldn't look exactly the same, because if it did, we'd still be using the Ptolemaic model of the universe, which worked perfectly well when measurements were very crude and the only thing we had to observe the heavens was the naked eye. Unfortunately, as measuring and observation methods improved, Ptolemy's model pretty much fell apart.
It could indeed look EXACTLY the same. But we would not be able to explain the motor of what was running in on gravity and simple rotational motion. We would have to add epicycles and other jigs and jogs to our explanation. The universe COULD be revolving around the earth, exactly as everything appears. But if it is, then Newtonian (or Einsteinian) gravity is not what's running it. Something else out there in the ether, perhaps intelligent phlogiston, perhaps something else, makes the planets do celestial loop-de-loos, double back on themselves regularly, etc.
You're right that it wouldn't look exactly the same and the rest of our physics be right. But if we postulate the earth at the center of the universe, we certainly can mathematically describe the motion of everything else...just not with neat elliptical formulae, and we would have to invent a whole new physics to fit the model.
To use Rob't of Occam's language, we would have to propose entities, many, many entities, as drivers to explain why the planets and stars do what they do. It remains POSSIBLE that this is actually right. The Earth really COULD be the center of the universe, dead center, with everything else rotating above us. But if that's so, then physics goes right out the window once you get into the stars, even if it works brilliantly close in. Obviously the earth-centered universe would be far, far from the simplest explanation that fit the facts. Kepler certainly made everything easier to describe and understand, and with a scalable model to boot. But Kepler and Newton could be oversimplifying. It could be that the Earth is the center of everything and that an intelligent clockwork makes everything act in funny, non-standard ways, and that everything indeed would continue to look exactly the same.
It's certainly not the simplest explanation that fits the facts. It's certainly multiplying entities to a high degree. Robert of Occam would NOT be pleased, and I doubt it myself, but who knows?