graphic styles as patterns

Would almost need to see the work to know which way to go. Expanding (Expand Appearance if the art has complex appearance) artwork lets you make it a pattern. Images need to be embedded.
In some cases rethinking the design and making several patterns then combining them into a graphic style can be a solution.

Both graphic styles and patterns can repeat and transform objects for a pattern to be able to repeat an object there has to be a "static" answer to it's appearance. The dynamic/live nature of Graphic styles especially when using an effect that has randomness as one parameter is not repeatable without compromising the randomness. Think of Graphic styles as your "Swatches for Appearance Pannel"

You may also need to ungroup.

Once you have a pattern tile, try Object > Expand before adding it to the Swatches panel as a pattern. You may need to expand ore than once.