Weather Band radios receive stations that typically are "on the air" on a 24/7 basis. Listening to both channels simultaneously or having two radios would, IMHO, be next to impossible. A scanner, by its nature, would merely stop on a given active channel and sit there until the carrier dropped allowing it to move on to the next channel.
Thus, listening via a scanner wouldn't be possible unless it had a feature, which some do, to pause on an active channel for only a given period of time before moving on to another. The result would be a very chopped-up conversation and not very desirable.