Not in what we traditionally think of as Ancient Egypt. The Egyptians preferred a tribute system to colonisation or conquest, mostly due to their religion. They believed that if you were not buried in Egypt, you would not move on to the afterlife. So Egyptians tended to go out, win wars, and then demand tribute rather than setting up new settlements or living where they conquered. There was a bit of a change to this policy under the Ptolemaic Dynasty, because they were Greeks and thus did not concern themselves with Egyptian religion by and large. Even then, they were more focused with warring with the Seleucids than founding new colonies.