Good question. I'm really not sure but I think the disk format
is independent of the number of bits in the processor, so I don't think it would be a problem reading from the drive. It really depends if the OS can read the particular format: FAT16, FAT32, NTFS, etc.. I see that there is a FAT64/exFAT(see exFAT on wikipedia
) but it's not related to the processor size. My mac mini can read a usb drive formatted for windows but it can't write to it. Back-in-the-day you had to buy a special program just to get the mac to read the drive so I guess I should be grateful. But I digress.
As a software developer, I would expect problems reading a project file created in a 32 bit version of a program in a 64 bit version, but I think most companies would resolve this before shipping the 64 bit version of the product. Depending on how the program saves the data it could work without a blip, could just not work at all or could "sort of" work but have weird seemingly random problems. A lot of programs now use xml to save their configuarations making them immune to these number-of-bits problems.
I'm pretty sure you would have problems initializing a new 64 bit system with a "system" backup of a 32 bit system (the os). The other issues I mentioned aside, I think you'd be able to restore "user" files from a backup drive but almost certainly need a version of the os that could tolerate 64 bits. You'd also have to reinstall any apps, and even get a new 64 bit version of the app. Could be a real mess. My friend was at his wit's end. I think I was the fourth person who tried to help him with this problem.