This is a GUESS so don't rely on this information.
But I am GUESSING that a FL .223 die, run in to a 5.56 chamber, would be similar to running a small base die.
In fact looking at the dimensions for chamber reamers, I notice that Clymer gives 5.56 base dimension as 0.3816", and .223 as 0.3794".
PTG Match .223 has a base dimension of 0.3779".
However, JGS and PTG 5.56 reamers are 0.3804" and 0.3803" respectively.
PTG's .223 reamer has a base dimension of 0.3804"...only one ten-thou larger than their 5.56 reamer!
But in general it appears that a 5.56 chamber will have a base dimension approximately 2 thou larger than a .223 chamber.
Therefore, I believe my guess is correct...running a full-length .223 die on a gun with an actual 5.56 chamber, not just a Bushmaster "maybe 5.56, maybe .223" chamber, should produce a pretty reliable base sizing.
But I do not reload for ARs and this is just a guess based on the base!
Looking at the dimensions of the various reamers nothing is jumping out at me to say there is any reason a .223 die should produce a cartridge with any difficulty chambering with any other dimension, but I am just scanning it. Base to shoulder dimension seems fine, shoulder angle seems fine...I believe there are no issues.