If I register, will I be able to open the unregistered files I made, and turn them into registered?
Yes
There will be a short dialog saying that if you save the file it will not be able to be changed by an unregistered program ... proceed anyway? In the future you would not be asked that when you save a file; it will just do it.
Just to confirm...after purchase, you should open any files created with the evaluation program in the full version. You should then save them. An informational prompt notifies you that the unregistered file will be saved as a fully licensed file.