There are reports of this in Chinese media, by the way.
I will admit the likelihood of this happening is very low. But the impact to the rule of engagement of a carrier is interesting.
US Philippine defense treaty only applies to territories ceded to Philippine by US -- so the US will not intervene on South China Sea disputes. However, if Philippine attacks/counter-attack using land based aircraft or shore based missiles, those may be subject to attack without invoking the treaty. So if Philippine wants to use air power without their mainlands subject to attack, then the carrier is the only option. Plus carrier is one a a few ways Philippine can do damage without being blow out of water immediately afterward.
If Philippine is able to pay for it and able to make it work, then it may be worth the money.-- it can at least make Taiwanese pause. However, those are two big ifs.
The point I am trying to refute is that this is Filipino propaganda, which it most definitely isn't.
And no, it won't. Anywhere the Principe could possibly reach and which the Taiwanese could possibly have any interest in (Luzon Strait, Pratas Island, Spratleys), the Filipinos can already reach with land based air-power with ease. Well, if they have any land-based air-power. Which they don't. And that's crux of the matter - Filipino military modernisation, if it ever happens will be a multi-decade process.
Indeed, wasting time on an old Spanish ship is actually
good for Taiwan - that means they have less money to put in the coast guard and the air force, two things which may actually have an impact in any future disputes, in favour of an undefended carrier which adds nothing to the table as far as Taiwan is concerned... except as trophy for Taiwanese captains, whose navy possesses 26 major surface combatants and dozens of FACs to the PN's... none.