No, it couldn't be locked in place.

1. If an exchange tried it, and the price was better on another one, people would go to that one.

2. If the government tried, there would be no practical way to accomplish it. Cryptocurrency is cryptography and hashes. More broadly, it is information and algorithms which validate the information. Information can easily have it's source disguised and it's content hidden from outside observers in a variety of well tested and standardized ways. It need not even pass through the internet at all, which is what a cold wallet is (on it's own), although it is certainly more convenient. Therefore the government couldn't fix a coin price either.