Sorry about the delay of someone responding to your query. If you haven't already done it by now, no you don't have to or need to partition any HD. I have Windows 7 32bit with a 500GB internal HD, not partitioned and 4 external HD's of which they are 1TB - 500GB - and 2x250GB. None are partitioned. Of the two 250GB drives one is a backup drive for the PC. The other is a Virtual Drive for Windows XP.
However, I don't recommend you carry all your eggs in one basket. I don't know what you use your PC for. But i mainly use mine for art, editing photo's and storage. All my work is contained on the other two external drives. The TB HD and the 500GB external HD. I keep the same material/data on both.
No doubt someone else will tell you something completely different. But at the end of the day the choice is your's. Hope this helps with your decision.