Narrow tires might help but there are a lot of factors that go into the rolling resistance of a tire. A google search on bicycle tires rolling resistance will give you an evenings reading. The rubber compound of the tire, the construction of the casing, inflation, tread design, etc all have a huge effect on the rolling resistance of a tire. But it is possible that you could find a wider tire that rolls just as well as a narrow tire. Now acceleration wise a lighter tire is going to help you in that area.

Shog