I've been told that it does because it's still searching for networks or something, which doesn't really make any sense to me. But what does fit somewhat with that are notices in the android interface that say enhanced location services will allow WiFi networks to be scanned for even when WiFi is off, though this isn't exactly the same thing.
All electric and electronic devices emit EM waves as a matter of course because changing current flows will produce waves like a motor, clock, or pocket calculator. But then there are also devices that intentionally produce emissions as part of their function like a radio.
Sort of like the difference between your lawnmower which produces sound incidentally compared to a speaker whose purpose is to produce sound.
If I check the devices using the router app on my iPhone, my iPad is shown as connected to the router.
Once I put my iPad into "airplane mode" then it gets removed from the list of connected devices in the router.
However, while it may not be connected, it could still be emitting electromagnetic radiation due to it being "on", so if you want it to have no electromagnetic signature then you would need to power it off.