[debowa]

I don't think it's a case of the squadron reapplying serial numbers, more a case of 'stopped painting them out'. Many Battle of Britain squadrons seem to have removed serial numbers from their fighters early in the war. In some cases they were reapplied at the time in very small numbers on the fin. When fin flashes were applied, these also disappeared from view.

This practice seems to have stopped before the beginning of the Battle of Britain so any aircraft delivered from then on are likely to have the serials in the normal place.
I'd therefore suggest that the key as to whether your chosen Spitfire has a visible serial is all down to when it was delivered to the squadron, roughly pre May 1940 no, post May 1940 yes.

Mark P