Is removing the SIM card necessary? When solving issues with tech support for various cell carriers, they recommend turning off the Android device, removing the battery, and then removing the SIM card.

Once the battery is out, is there any effect of also removing the SIM card?
Removing the SIM card might help the phone to flush out cached  data.

Other than that, I see no reason why removing a SIM card would change anything. The general purpose of those instructions is to hard reset the phone (without any data in RAM).