Not necessarily. There are
certain optimizations made possible by the current structure of the block header.
ASICs don't compute SHA256 anyway. They compute a vast number is parallel without any flexibility at all.
If the header was changed (say to move the nonce), then ASICs would be useless. They might be able to handle a change in the size of the header (up to around 120-127 bytes), but the nonce must be in the correct position. Otherwise, the ASIC wouldn't be set up to increment it properly.