No you wouldnt. Both d800 and 5d3 sensors have better high iso purely because they have 2.5 times the surface area of a crop sensor.
Cropping the D800 sensor gets you a d7000 sensor, which is very close to the 7d at high iso ( a touch better is all).
I'm very aware of the size difference. But...
I would be willing to bet money on it not being so simple. It would have a lot more to do with the size of the photo receptors (pretty sure that is the right term), and the tech. Both the original 5D and the D700 have 12MP sensors, right?
From actual files, I have compared with friends cameras, the D700 kills the 5D in high ISO. But the sensor size is the same, as is the mega pixel count. According to your argument, both should have the same high ISO performance.
So tech makes a difference.
The sensor size just means you can have a high megapixel count, with larger light sensing receptors. Larger receptor would, as far as I can see, result in better low light performance. Then there is the tech - and I'm pretty sure the D800 is newer tech than a D7000, but I'm not altogether sure on that one.
By your reasoning, all FF sensors would have identical high ISO performance.
Now, I have yet to see a crop sensor, made with the SAME pixel density and the SAME tech as a FF sensor, but I'd be willing to bet that if they did, the high ISO performance would be near enough identical. OF course, you'd have less megapickles on your crop sensor, along with all the pros or cons of a crop - except, it would actually be a crop, in every sense of the word, not just field of view and sensor size description.