All of the HFS (Mac)-formatted non-Time Machine partitions, yes. I suggest blacklisting your non-essential files, though, unless you have tons of space on the Time Machine drive. Backing up two drives to one may prove problematic as Time Machine doesn't make compressed backups. If you're trying to back up two full 500 GB drives, your Time Machine drive should be at least 1.5 TB to account for versioning.
I suggest buying a dedicated external drive for Time Machine. Maintaining a backup is a good idea for many reasons, and an internal backup drive won't help you if the computer is stolen or dropped, or the PSU surges and fries all of the drives in your box at once.
Since hard drives only have a limited shelf life, it's a good idea to leave your (external) backup drive off most of the time if you don't use it for versioning as well as traditional backup. Your system will remind you if you haven't made a backup in 7 days. And no, Time Machine won't back up while your computer is sleeping.