Not sure I understand the specific benefits of using this script - compared to simply scp-ing the public key from the command line - but if a GUI popup for entering the password is preferred... why not.  Looks like a reasonable implementation to me.

As to compromising security, I think it depends on how paranoid you are. The more the password gets passed around, i.e. the more locations in memory it'll ultimately be left behind, the easier it might be for someone to get hold of it... Whether that's an issue, depends on the particular circumstances, e.g. if this is a private machine of yours in a secured environment, and you're the only user, etc.