I can hear the one on my SYM and the one on my Suzuki so I'd say that it should be audible.
Had a friend who had a 250 like yours, but i don't recall the fan specifically on it.
Usually only an issue in traffic or extended idles or climbs on anything I've had.
The time I had a similar issue on my Burgman I ended up tracing wires after checking fuses and the like.
No fun at all, but the parts cost on the fix was cheap.
There's a 10amp fuse for the fan you may want to check, make sure you have a couple spares since it may have blow for a reason...and back to wire tracing.
at this point see if you can get that cover off and get an eyeball on it. You may get lucky and see an obvious disconnect pr obvious corrosion right at the fan or in the immediate harness.
BTW I did a google search for Xciting 250 fan repair and saw a link for a pdf off xcitingclub.com that was for the cooling system.
Download and check at your own risk of course, but when I looked it over this does cover the fan including some pics.
I ran it at idle until it overheated in my yard, I definitely did not hear a fan. Is it obvious when it's running, like a car?
Thank you very much for that, I'll take a look tomorrow.