Yes you can delete the content of the default file geodatabase, ArcGIS will keep functioning correctly. You can even delete the entire file geodatabase and when you start ArcGIS again a new one will be created.
Now, before you delete the content or fgdb, it may be wise to ask yourself why there is 30 GB of data inside your file geodatabase. When you start geoprocessing or generating results, it is good to create a file geodatabase in a project folder and store the results there with understandable names. You may have MXD's referencing the data in the default file geodatabase. So be careful with what you delete.
Are you using a lot of raster map calculations? Did you look at the content of the file geodatabase?