No, it will only be formatted one time- and that is only needed because virtually all external drives come pre-formatted for use with PCs (either a NTFS or FAT32 format). Time Machine requires a drive formatted in a Mac format (specifically Mac OS Extended), hence the request to format before starting a Time Machine backup.
After formatting, the drive will be able to be used for anything you would like to store on it with your Mac. Time Machine keeps its backup files in a separate folder on the drive so as long as you don't try to store anything within that folder you will be fine.
Do keep in mind that the files you store on the drive alongside Time Machine will not be backed up however since TM obviously does not back up the drive its backups are on. If you would like those files backed up, you need to prepare your new drive by making two partitions on it with Disk Utility prior to use-- one for the Time Machine backup files and another for your file storage. Time Machine can then be instructed to include the second partition in its backups.
If you need some assistance with partitioning, the following is copied from the Disk Utility's Help menu entry (my additions are in
red):
To partition a nonstartup disk:
If youre partitioning an external hard disk, make sure its connected to your computer.
In Disk Utility, select the disk in the list (on the left) that you want to partition.
Click Partition (in your case choose "2 partitions").
Choose the number of partitions from the Volume Scheme pop-up menu.
Click each partition and type a name for it, choose a format (choose Mac OS Extended (journaled)), and type a size. You can also drag the divider between the partitions to change their sizes. If a partitions name has an asterisk beside it, its shown larger than its actual size so its large enough to display its name legibly.
If youll be using the drive on a Windows computer, click Options, and choose the Master Boot Record partition scheme (also known as fdisk). (Actually, do that anyway and choose "GUID" to change to an Apple partition map since your disk came formatted for Windows)
Click Apply.
If you have other questions ask away- somebody will be happy to answer!
