It does and it doesn't at the same time; when you open a second app the first one is left hanging up on background. You can open lots of apps, but almost all of them will just freeze on background until you bring them back. Almost all of them, 'cause WP8.1 allows apps to be suspended instead of closed when you hit the Back button (like Facebook and Calendar). Resuming a frozen app can be a very small issue on 512 mb devices, as heavier apps will display the ''resuming'' message when you get back to them. I don't think the L820 will get many of those messages.
you can however set which apps can run on background on multitasking - like Whatsapp, for example. Even if you close it or open another app, allowing it to run on background will not stop it from getting new messages. Check ''Battery Saver'' on app list or settings menu to configure background process