Thanks for the replies so far! Indeed common sense might dictate that anti-ice is to be switched off but I am very surprised this is not mentioned anywhere (as far as I know). However, bleed air is always extracted anyway for engine turbine cooling etc. So maybe it is not such a problem anyway to keep the anti-ice on?
My worry is still sitting there in heavy icing, with engines running for a good ten minutes whilst the airframe is being de-iced without any ice protection for the engines.
a5-in-the-sim, we have similar engines (CFM)