Mike,
They can coexists but best to run AC anyway. Corallimorphs are very noxious but zoos are not so. The zoos multiply intensely to out compete other corals and tend to grow over anything and everything. They also have a very potent sting that is very harmful if you touch them with an open wound and if you get their mucus on your eyes, so be careful when handling them.
According to Anthony Calfo, mushrooms are really noxious:
"But I cannot overstate their aggression enough. Among the 100+ corals commonly kept in aquaria... corallimorphs "mushrooms", "star polyp" (Briareum in the hobby lit) and encrusting gorgs (Erythropodium) are easily top 5 most noxious. They are just brutal."
http://forum.marinedepot.com/Topic62493-4-1.aspx