You'd better call them to be sure, but I figure they should, since they manufactured it!
FYI, I brought my A1 to KM service centre last month, and was told the CCD would be replaced for free, but I would probably have to collect it from Sony mid-April. A week later they called and said the replacement CCD wasn't available, and gave me a replacement A-200. After using it for a week, I'd rather have my A1 back
If Sony offers you a replacement, ask for a DSC-R1 instead -- even if you don't like it, you could probably sell it for more!