No, no no. Overkill software don't give payday 2 for free. They are making hundreds of dlcs to get the money for everything.
But who knows, we made 1500000 players in steam group, and overkill tells that they give 'secret stuff' for free. Maybe it is payday 2 for free.
Anyway i can recommend you payday 2. It is great game, where you can do heist in stealth way, or full aggression. I spend almost 550 hours in this game and i am still not bored. Personally i think that is the best co-op game ever. And many of L4D2 players likes payday 2 too.