How specific are ASIC's design? Can they single hash SHA256? I understand that Bitcoin's ASICs are a highly optimized piece of equipment and, therefore, are also very specific.   

My question: are they able to do a single (or triple?) SHA-256 hash at all? And, if so, how competitively would they be with versus a GPU?
A Bitcoin mining ASIC: 


does not attempt to complete a single hash, rather fragments of two SHA256 compression rounds which is then compared to a target, the result is never returned 
can not accept arbitrary information that is not in the form of a partial SHA256 compression round


So in terms of competitiveness, a CPU can actually complete a SHA256 hash, a mining ASIC can not, which I suppose puts it ahead in this arbitrary race.