NO! That's potentially even more disastrous I'm afraid! You can only move user data files basically - music, movies, downloads etc. You should not need more than about 40GB for your entire op sys and installed apps so it should not really be a problem.
You can't simply move Program Files to a different drive, your installed software won't work. At some point in future, you may want to start installing software to your external drive instead of C:\Program Files.
You can mange easily with using the whole of your 40GB for your op sys and programs - just store all your data files on the external drive. If you're getting or already have another drive a second option would be to replace the internal drive with a bigger one and use the 40gb drive for an external.
If they are the same interface I think I'd exchange the two of them, using the larger drive for internal storage, partitioned to 40GB system drive and 120GB for data and installing the smaller one to the external case for backup.
It is important to note that the reason why you cannot simply move application and Windows files is because moving them does not update the Registry with new locations.
That said, moving most applications can be done without a complete reinstall (I don't recommend moving OS files).
If you have Microsoft Office, for example, you can move (cut and paste) the folder. Then run install and tell the routine to install in the new location. The install program will see Office is there, and prompt to "fix" it. Say yes, and it will update the Registry for the new locations, without losing all your customizations.
Again, don't try this with the OS files - just the programs you installed.