To answer your question right away, yes, you can have the EH3 NC 3.5 mm wired AND have ANC working! ....but:
1) You have to first switch the headphones on and then connect the 3.5mm wires. If you first hook the cans up with the wires, the EH3 NC won't swich on!
2) and this is just a first experience/guess of mine: since you are not establishing a successful Bluetooth connection between a source device and the headphones (because you dont need/want it in wired mode anyway), my EH3 NC switched completely off after 5 minutes (which was the idle time I set in the app when there is no Bluetooth connection)!! Nevertheless, the audio in the Youtube video I was playing of course continued to be audible due to the wired connection, but the ANC was of course gone.
So, that was quite some learning...
EDIT: You can permanently switch OFF the idle time mode when you move the slider in the FiiO Music App to the very left! In that case, the headphones don't switch off at all and ...there you go!