Your absolutly right; it all depends on the BIRDS themselfs. since i have never had parrots, all i can say is ALWAYS SUPERVISE. they may fight they may not. good luck.I would say that it just depends on the individual bird(s). I would feel it out.They MAY be able to free-fly together,pending no agressive signs from the macaw/teil, but i would cage them in seporate cages for sure.
My jenday conure does wonderful with my other birds.I have seen the same species of conure tear off another ones beak.Its individual temperment more than species.