Nope. Any phone capable of running 2.2 doesn't need a task killer. Android was built as a mobile OS, so you can't think of it in desktop terms.
Here is a video by Google that explains how Android memory and cpu really well. However, it's a video aimed at developers, not end-users, so it may end up just sounding like technobabble to some viewers:
https://www.youtube.com/watch?v=fL6gSd4ugSI&feature=player_embedded
The short of it is: Android handles all memory and cpu allocation just fine. There really isn't a need for a task manager, especially on 2.2.
If you're interested in the guts of Android, I really recommend watching the entire Androidology series of videos:
https://developer.android.com/videos/index.html#v=QBGfUs9mQYY
I truly believe the only time a task manager is useful is if you have one app in mind that you want to keep on your phone, but don't want running itself. Any other use would just be shooting yourself in the foot and you would be sacrificing efficiency and performance in your quest for efficiency and performance.