It would still be mostly "constant". The ASIC would still just vary the 32-bits of the nonce (so 4 billion hash checks). The question was if the data after the nonce has to be all zeros, i.e. is it hard coded into the ASIC that the header is 80 bytes long.
It is a what-if mainly. I was just wondering if there was any point in even considering a header size change.
If ASICs require an 80 byte header, then that pretty much brings the discussion to an end.
The fact that old clients also require an 80 byte header also acts against it.