It could, but it surely would be easier on the actor. I've always hated the 'confrontation' where the actor has to suddenly change back and forth between characters, it always sounds stupid live, whereas on some of the CD's it is clearly recorded seperately, even with some overlapping at times. I'd always imagined (atleast i this part, if it is played by the same person) that the Hyde parts are pre-recorded and the scene is set on the street infront a shop window and he is argueing with his 'reflection' which would be a 'double' behind the glass, that way you would get the effect you do in movies where the reflection suddenly starts to move and act differently to the person the reflection belongs to.
http://www.flickr.com/photos/27199361@N08/ Phantom at the Royal Empire Theatre