You are right in your suspicion: a 32 bit version cannot be updated to a 64 bit. If indeed your backup is up to date, you have no actual risk to loose your personal data.
Whether you will need to reload your data on your computer or not fully depends on how your system is configured. In a default installation, the root partition and the home partition containing the user data are on the same partition. When you install a 64 bit version over your old 32 bit version, you will typically reformat the partition, hence also wipe your data. Some users have a separate partition for /home. In that case, wiping the system partition leaves the user data on the other partition intact.
In theory, you could install your 64 bit Ubuntu on your current partition without reformatting. Then your data would remain. However, you would be left with a lot of orphaned system files from your old system. Old configuration files might interfere with the new installation. Therefore, this is a no go. The right way for you now is to have a good backup of your data, wipe the current installation for the new one and restore your data when the installation is up and running.