Well I have experience of going narrower and in my case it made a difference.
I was driving a Merc W124 E-Class coupe a bit like this one:
File:Mercedes W124 Coupe rear 20071022.jpg - Wikimedia Commons fairly slippery but heavy and it had low profiles on it.. as the car aged and I didn't want to spend all my money on tyres I decided to back to the narrower and higher profile stock tyres. This added ~5% to my FE.
So if you drive, say, a large but unloaded Van then your Cd will dominate, if however you drive, as I do, a relatively aerodynamic but heavy car then Crr will show itself.
Added to that is speed, if you always drive well above the point where Cd>Crr then dropping your Crr will not make much difference.
Derek