When turning on the Anti-Ice, the demand for bleed air increases and the EEC (Electronic Engine Control) will increase the target N1 to provide enough pressure by injecting more fuel. From the Boeing 737 NG FCOMv2 (7.20.5 Engines, APU - Engine System Description, emphasis mine):
In the normal mode, the EEC uses sensed flight conditions and bleed air ...
Turning on Engine Anti-Ice causes the engine idle N1 to automatically increase so that it can supply additional bleed air and not flame out.
This means that for descent planning, an earlier descent should be planned since idle N1 is now producing higher thrust.