Since no one answered I watched all of the movies myself. The answer is yes. While at first glance the story in the movies might not have anything to do with main story, however, it does set up the events that will lead to season 3 such as returning characters and new characters. The order I mentioned above is chronological order (switch case 1 and 3 though) but I'd recommend everyone who is new to watch it in a release order that is.
- Psycho-Pass 1
- Psycho-Pass 2
- Psycho-Pass: The Movie
- Psycho-Pass: Sinners of the System Case 1
- Psycho-Pass: Sinners of the System Case 2
- Psycho-Pass: Sinners of the System Case 3
- Psycho-Pass 3 <- Currently airing at the time of post
If you want to catch up fast you may skip Psycho-Pass 2 and Case 1 and 2 since they are least important. In my case I haven't watched Season 2. All three movies were hour long so it doesn't take much time to watch them all.