That is indeed a very valid fear. Been there, done that. Coccidiosis is a very high risk any time you introduce new birds to a flock or when you first put brooder raised youngsters outside, all birds involved are at risk. So you need to know the earliest symptoms and be ready to treat asap or just go ahead and treat preventatively. Keep Corid on hand. Aside from that, yes, the risk of the older birds bringing along some other kind of disease is also high. You should quarantine them a minimum of two weeks, 30 days is better, so you can observe for any signs of disease. Very often the stress of moving to a new home is enough to cause carrier birds to have a flare up. To be honest, I'd far rather get more day old chicks and raise them then bring home adult birds to add to a new flock of youngsters. In fact I do not ever bring home adult birds anymore just for this reason. If I want new birds I get day old chicks or nothing.
Make sure you introduce everybody properly when you do get ready to integrate them all. If you just take the youngsters out there and stick them in with the older birds they are likely to be severely attacked. Chickens hate newcomers and can be quite brutal, even to the point of killing new birds. Very young birds are at a much greater disadvantage. Having a lot of space and lots of places to hide is very important as no matter what there will be pecking order scuffles.