Since it's always nice to have a second opinion, I can confirm that this is, indeed, the case. The EA DL Manager DOES NOT need to be running to play.
The EA Download Manager (EADM) basically just download and installs the files. That's ALL you need it for. You can run games without it actually running. Makes sense, since they sell their games every avenue [digital and retail] that they can.
A lot of EA's recent games, you can just register right through their EADM, if you like - and just deal w/ EADM.
If you need to back-up your EADM game, it don't keep installers anymore - so you don't have extra installer files and junk laying around to take up another extra amount of GB's. This all is much more streamlined, for the better - you'll just can copy your actual entire game folder as is elsewhere (DVD's, Blu-Ray's, another HDD, whatever).
When you want to reinstall game, take your copy of the game folder - and look for a INSTALLER sub-folder. All you need to do is run the SETUP file(s) that's in there and you're good to go.