I have a internal drive containing 640gb of storage with the operating system on it, my external time machine drive is ~720gb. I am thinking about installing another internal 1tb hard drive, and still using the external drive I have. I am guessing that it will backup until there is not enough space on the external drive. I am not going to backup all of the folders to the drive so the two drives combine (both internal) should never reach 720gb. Is my hypothesis correct? Can time machine handle this?
Yes, Time Machine will backup until it fills the backup disk and then it will start overwriting old backups to make way for new ones. However, if the volume of data you've told Time Machine to backup exceeds the size of the disk Time Machine is using to save the backups on, it will complain that the disk is too small. If you have a Time Machine disk which is smaller than the combined size of the hard disks used by your Mac, it's likely you'll need to manually intervene at some stage due to this issue unless you're very diligent about ensuring that you don't ask it to backup too much data.