It is important to distinguish between airframe/cowl icing and ice crystal icing. They are not the same thing, yet the use of engine anti-ice in some cases of ICI is recommended. From the 2011 Boeing Flight Ops Technical Bulletin regarding ice crystal icing:
Q9. In these conditions, should engine anti-ice be turned on for all aircraft?
Not for all aircraft. Engine anti-ice supplies heat to the cowl and, in these conditions, that is not where ice is forming. Engine anti-ice also has other effects: Accelerating the engine to approach idle, providing ignition, and promoting a higher fuel-to-air ratio in the combustor. We have recommended using engine anti-ice for only those engines where we believe these effects are beneficial – those engines that have a power loss during low power. If the power loss or damage problem occurs during cruise, none of these effects prevent icing-related power loss.
The entire Bulletin can be obtained at:
http://www.dispatcher.org/images/Lib...stal_Icing.pdf