If SHA256d is "run it through SHA256 twice" then in theory it could be made to work with an ASIC via a rewrite of the software that runs the ASIC - but not sure how efficiently it could be done.
Probably fairly good efficiency if the code is set up correctly and if the ASIC is designed to handle one piece of SHA256 data at a time rather than processing blocks of SHA256 data.
No rewrite would be needed, though, because bitcoin and the ASICs used to mine it are already doing SHA-256d. In fact, I'm not even sure it's possible to use most ASIC hardware to do only one hash - everything does it twice. Probably fairly good efficiency if the code is set up correctly and if the ASIC is designed to handle one piece of SHA256 data at a time rather than processing blocks of SHA256 data.
