It's capable of basic, stay-loaded-in-the-background multitasking, but not currently of background downloads, and that's actually intentional - downloading add-ons sucks up most of your iPhone's bandwidth, and extracting / installing them most of its processor power / I/O speed, so we were worried that people would have a hard time doing other things they wanted to do with their iPhone when they exited Pleco while downloads were still running. Plus, background tasks are automatically killed after 10 minutes unless they're in one of a few specialized categories (podcasts, etc), so for long downloads you'd have to keep going back into Pleco to get them to finish.
But it does handle being put in the background gracefully - it suspends all downloads, makes sure the files are all written out to disk and their current download states saved - so that if you or the OS subsequently kill Pleco in the background (or even, say, turn off your phone) it'll still be able to resume them when you reopen.