lol, no one can come close to hainan to collect anything nowdays.
No, foreign spy planes can still fly very close to Hainan and while China will still intercept them and escort them and maybe even buzz them closely China cannot shoot them down to deny them from getting close enough to conduct ELINT or SIGINT.
But that's beside the point -- if your proposal is to send J-20s to Hainan, then it is likely that much of their purpose there would be to operate in international airspace either as interception/escort role, or simply conducting training over the SCS, so it won't matter if foreign spy planes are operating in international airspace off Hainan, because the J-20s will probably be flying in international airspace themselves if they're based there.
Operating the newest fighter of the Air Force, and a stealth fighter at that, in international airspace will almost definitely invite opportunities for foreign militaries to collect a substantial amount of information about the aircraft relatively early on. I suspect the PLA would prefer to keep as much info about the J-20 close to its chest for as long as practically possible.
Deploying the first handful of aircraft there would also be counterintuitive to other needs such as defending higher importance regions on the mainland such as the capital, or major economic and population centres, not to mention needing aircraft to provide operational training and to develop doctrine.
So while on the surface it is an attractive idea that deploying the newest stealth fighters to Hainan to provide backup in the SCS domain it's probably not a very logical one.
It would be much more sensible to deploy J-20s to Hainan once they have a much larger number of the aircraft in service, probably after they have a regiment dedicated to operational training and doctrine, and three or so regiments for the more northern and eastern parts of China, until which they could probably consider raising a regiment dedicated for the SCS.