What will happen if I lose my Internet connection when I play the game?
If you lose your Internet connection the game will pause while it tries to reconnect. If the Internet Connection is unable to resume you can continue the game from where you left off or from the last saved game.
Will I need to be online the whole time when I play the game? Including for single player?
Yes. You will need to have an active Internet connection to play the game, for all game modes.
In light of the experience of PC Gamer's reviewer, I interpret these 2 statements to mean that you can indeed resume from your last save, as soon as you can reconnect to the internet. The reviewer even provided an MSPaint rendition of what he saw when losing his internet connection. It didn't seem to leave any options beyond connect or save-and-quit.