This is something I doubt. It would be rather easy to change the software and make it sync passwords, even on an individual basis. If this would come out, it would mean a big marketing problem, and could result in sales losses like 10-20%.
I said "could", but to be honest I think 2-3% is more realistic. Most people don't care. They want their data to be safe in case of theft, and have a backup in case of loss. Here on HN it's a big thing, but most users don't know, don't care.