To answer your question, no.
However, very few of the apps in the "Recents Drawer" are actually running in the background. If you've been experiencing slow operation, you might wish to investigate other causes.
You can test my opinion by manually "X-ing" out each app in the "Recents Drawer" and then opening only one app that displays the slowness that you're investigating.
I don't fully understand what the System Reset does but I've found that it cures many ills. It's easy, quick and harmless:
Hold down the on/off switch and the Home button simultaneously until you see the Apple logo. Ignore the "Slide to power off" text if it appears.
A System Reset does not remove any apps, music, movies, etc. nor does it cause any settings to revert back to default. It will, however, shut down any apps that are operating.
Also, you might wish to download the iPad-2 User Guide. Pay special attention to page 162. Note that this Guide also applies to the iPad-1 with IOS 4.3 except for those functions that are not supported by the hardware.
http://support.apple.com/manuals/#ipad
Finally, the User Guide can be downloaded at no charge via iBooks and a less comprehensive version of the Guide is included as a Safari bookmark.