Yes, this glue is important. E.g., the VP dropping by the EM's staff meeting to give a tailored version of the message and do some Q&A, and the VP doing skip-level 1:1 meetings to get the perspective as seen by the EMs. If you build kind of a mesh of redundant communications, you can better course-correct (which also means correcting the original message after observing its actual effect on the team).