Yes, it does improve FE a bit, but as it turns out at a very high price.
A couple of weeks ago I had my '07 HCH in for its 45K maintenance work. Everything was fine -- except for the rear suspension, which had to be replaced, along with the tires. The culprit: overinflated tires (I was keeping them at 38-40 psi). Fortunately the car is still under warranty and I'd signed up for the dealer's "tires for life" policy, so I wasn't out any cash. Otherwise, the suspension cost alone would have more than negated any gas savings. Even worse, the new suspension & tires have essentially put me back into "break-in mode." My 1st tank afterward was an abysmal (by my historical standards) 49 MPG, and today's was a still-subpar 52 MPG.

(Click on the lower banner for this car's history.)
Lesson learned: Don't exceed 35-37 psi. The cost-benefit ratio is in the wrong direction.