You didn't indicate what you want to record from your screen. If it is Movie Edit Pro for making a tutorial or something, then this program will not work well. You would have to open 2 instances of MEP, which becomes very heavy for the computer.
If it is for something else, then you should look at other programs that are much better, some of them have free versions, like Debut.
I wouldn't upgrade MEP just to get this feature, however upgrading is a very good idea if you plan to do a lot of video editing, as you soon run into limitations with the basic version.