Getting the blood flowing and muscles warm before beginning to throw is the goal. You can do that without bands if you want. The bands are a tool that make it easier and more efficient for many, but ultimately you don't need them.
Using the bands for strengthening is a little different. Again, you can do the same movements with weights - but bands make it much easier.
As was mentioned before, the Thrower's 10 is a good base set of exercises for the arm/shoulder. It works very well with bands or small weights. My son has been doing it at his PT's direction every day. On days where he pitches, he cuts the reps and resistance and uses it as a cool down.