Yes, that particular drive should be OK for backing up your iMac. However, it will not operate at USB 3 speeds as your 2011 iMac is USB 2 only. And yes, it has to be re-formatted as the drive comes factory formatted to NTFS (Windows proprietary format.) Formatting it is easy with Disk Utility. Be sure to format it as Mac OS Journaled (HFS+) GUID partition scheme. (should be the default) You can use the drive for Time Machine backups.
I also recommend you make a clone backup using either Carbon Copy Cloner or SuperDuper on another separate external hard drive. That way, if your iMac drive goes bad you can replace it and then clone back from the external. By the way, your 2011 iMac uses a Seagate 500 GB hard drive which have been problematic. I had the same exact machine as you and my drive failed after two years of use. Fortunately it was covered by extended Apple Care and replaced for free by Apple.