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As the OP said, the biggest problem is blackhead, a protozoan disease that chicks are mostly immune to and poults are very susceptible to.
"Blackhead (Histomoniasis, Enterohepatitis)
Blackhead is an acute or chronic protozoan disease of fowl, primarily affecting the cecae and liver. The disease is present wherever poultry are raised. Blackhead is one of the critical diseases of growing turkeys and game birds. It may cause stunted growth, poor feed utilization and death. It is of lesser economic importance in chickens since they are more resistant, but the incidence in chickens apparently is increasing.
Blackhead is caused by a protozoan parasite called Histomonas meleagridis. The organism in passed in the fecal material of infected birds. In many instances, the organism is shed within the eggs of the cecal worm of chickens, turkeys and game birds. Free-living blackhead organisms do not survive long in nature, but those in cecal worm eggs may survive for years. Therefore, most blackhead transmission is considered due to ingesting infected cecal worm eggs. Transmission may also occur by the earthworm.
Chickens are frequently infected without showing signs of the disease. These chickens may shed enormous numbers of blackhead organisms, many of which are protected by cecal worm eggs. Outbreaks in turkeys can often be traced to direct or indirect contact with ranges, houses or equipment previously used by chickens."
http://www.msstate.edu/dept/poultry/disproto.htm
They can be raised together, but it's best to keep an eye out for problems. In my experience they end up going their separate ways in adolescence.