You will not be able to use any image backups as those would restore your 32-bit system, but the file backups will be available. The file backups only contain data, so that is not affected by which version of Windows you run. Just make sure you only format the C: partition when you do your clean install.
Edit: Note that if any of your file backups contain installation software, that software may not install to 64-bit windows. Most software does, but there are a few 16-bit applications that work in 32-bit Windows, and 64-bit Windows cannot support 16-bit software.