You aren't able to claim APD vehicles as stated by Noodles and Brolad above, however you're able to claim all armed/armored civilian vehicles (illegal vehicles).
The DLC is only required to play on the map and campaign, you are still able to play with the weapons, gear and vehicles as with any other dlc however you'll just get the usual pop up ads.
When starting the Arma 3 launcher, try setting your parameters to enable static background, which disables the world in the background of the menu.
Nevermind, doesn't work :p