Is it "mandatory" to partition a hard disk for use with Mac OS?
If you zero out the drive, it means that you've completely erased the drive, partition map and all. The partition map tells the OS how a drive and its' space is used, and in order to use one to install and OS to or store data on, it needs at least 1 partition. If you've used OS X's built in Disk Utility "Erase" function, it asks for a new name to rewrite the new partition as, which means you shouldn't need to partition further. Additional partitions are useful if you ever plan on dual booting or want to keep certain data in a separate area of the drive.

Also on the note of wiping a drive in an attempt to get it working after it has bad blocks. It is generally not a good idea to do since it means that for one reason or another the data there has gotten corrupted. It could have been particulate or dust on the platter, a head crash, driverboard failure, or any number of things. Once a drive is found to have bad blocks at all, I would advise backing up or recovering as much data as possible and replacing it as soon as possible.