As long as both the source and the destination folder are owned by you: yes, you can.
The problems start when you want to access other user's directories or even the system ones (like /usr, which doen't have anything to do with users, it is a system-wide tree).

PS: with terminal commands you will get "Permission denied" errors too, but in the terminal you can use sudo or even become root yourself to have the right permission.

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If you want to use GNU/Linux but want to avoid using the terminal, take a look at Elementary OS. It's my understanding that one of the goals of the system is to allow the user to avoid the terminal as much as possible (though I haven't tried it myself because I don't need or want its features).
Also, if your problem with typing terminal commands isn't physical in nature, then you should know that they are fairly intuitive after you get some practice and one of the great things about Linux is that there is extensive documentation for a lot of software that can help you to understand it. If you have a physical obstruction making it difficult to type, then again, Elementary would probably be your best bet for a Linux distro.

^ The problem OP was experiencing in this thread would have been exactly the same in elementary.

Obviously it would. The point is that the terminal is less necessary there, which directly answers the OP's larger issue with executing terminal commands (which is not confined to this specific problem).