Yes. Once you have the fully licensed version of the program, just go to the preferences and delete the rendered files and media cache.
Media cache files are not involved in the removal of the Adobe watermark from the project.prel file from a tryout.
Just a re-enforcement mention...you cannot remove the Adobe watermark from a tryout "saved" exported product; whereas, you can from a saved/closed project file (project.prel).
By exported product, I mean a burn to disc in the tryout or the Timeline of the tryout exported to a file saved to the computer hard drive.
In the case of removing the Adobe watermark from the tryout project.prel, classically you delete the rendered files (Timeline Menu/Delete Rendered Files) in the purchased program. In no way is media cache involved in this. Some of us have found that there was an automatic removal of the Adobe watermark resulting from just opening the tryout project.prel file in the purchased program.
Please review and consider.