yes, it is safe to put two day olds with one week olds. You can put them together up to a couple weeks...just keep an eye on them if they are past two weeks. I have had some older ones actually spread their wings and younger chicks run to them for a snuggle
I am sure it depends on the temperament of older chicks and breeds? I wouldn't hesitate at the age you are talking about.
I put 1 week olds in with a 4 week old Faverolle. Might not work with other breeds. Faverolles are very mild mannered chickens. Also, the Faverolle was a little small for her age. They have been together for 12 days now.
Also mixed 6 week old Ameraucana chicks with 1 week old Buff Orpingtons. That was in a larger space than a brooder. They all did fine. Again, all were gentle breeds and the space was 40 sq. ft. with a light at one end. They all slept together near the light even though the older birds did not really need the light.
I put a wire divider between the two sets of chicks for a couple of days so that they can see each other and then take away the divider. I use dog carriers for brooders so I just put the top and bottom facing each other with the wire door separating the two sections.