I think it makes sense, and then it also adds the extra drain for the cloak. They really DIDN'T have power for the shields and weapons while cloaked and running at warp. I could easily see how a 'impulse fueled warp system' would keep that drain going.
Then, an easy thought, when true warp cores were added with the D-7 systems, the cloak's required power went up exponentially to deal with a much more profound warp signature.
Not sure how to model this well in CODA. I'm still going through the ICON material I got for a few bucks at the local game store.