WBT in general, sees student engagement as resulting from good student motivation. They are cause and effect, not necessarily the same thing, at least in my opinion.
You can really think of WBT as having two major components. Classroom management, and teaching methods. The WBT classroom is most fun and effective when you are using the two together as an integrated whole. I know of teachers who favor using one part or the other.
Personally, I find it much more effective to use both components. The classroom management portion is strongly constructed and provides a coherent set of interactive supports between all its sections. The teaching methods are based on the latest in brain based research for best practices for teachers.
I teach middle school science and social studies, and college level history. In my college class last semester I had one student who commented that he had been through an orientation on the way college classes should be taught, and in three years my WBT based class was the ONLY one that followed the guidelines he had learned as the most effective way to learn for the students- cool, hunh?
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In my opinion, you can have classroom management without student engagement, but student engagement will almost take care of classroom management. There are teachers that have a very conventional, structured class where everyone follows the rules and raises their hands, but the kids are not truly engaged. It is impossible not to be engaged as a learner or teacher with WBT and that will take care of most classroom management issues. 
