Hey Jonathon, just adding my two cents as I went through this 2 weeks ago.
I had some three week old chicks and brought home some 2-3 day old chicks. I put them all together and the 3 week old ones (especially the top male) started pecking the little ones on the heads and chasing them into the corner (away from water, food, and the heat lamp).
I am sure it depends on your birds and perhaps the breeds. For me, I wasn't taking in chances. I got another heat lamp, food trough, and water container for the little guys. I then divided the two areas of the brooder with a large (high) piece of cardboard. Since these chickens will eventually have to interact, I cut a small hole in the cardboard big enough for the new chicks to go into the "Big Chicks" area, but NOT big enough for the older chicks to go into their side.
It has been about two weeks now and everyone is getting along great. The little chicks still hang out on their side when they sleep, but go back an forth all day long. Just remember to keep adjusting the size of the cut out as the chicks grow.
Hope that helps.
Chris