An insulated F/B shouldn't change the rate of burn so I'd say "no". It's likely a smaller fire will be needed when compared to a standard box - that may actually require more frequent addition of splits to maintain your coal base. I add a small split about every 30 minutes with my insulated F/B set up. Simply put, you'll use less wood in the long run.
This pitmaster talked about the pros/cons of insulated verse partially insulated fireboxes. I thought it was pretty good. His fire management lesson is also on point.