As mentioned before, I was unable to play the demo online at all. After purchasing the full game, I tried playing it with the same friend again online. After installing the 1.10 patch, we managed to get into the game no problem. There was a lot of lag though, even though both of us have great connections (fiber optic and ADSL2+ respectively). Still, these are EA servers and it comes as no surprise, but the lag is much worse than it was in the original Army of Two. It was bearable anyway. Note the "was".
Next game session a few days later. Had to install the 1.20 patch and was hopeful it would improve the online play. To my utter disbelief, the patch has caused the same problem as the demo and we are now unable to play online. I will try again soon, but it doesn't look good. The only reason we bought the game, was to play it co-op online. I will be sure to update again.