i dont think so.
Again, nobody thinks the Argentinians will be able to successfully take islands, not without years of build up and billions that they don't have.
but you still have to track and following any movements by the Argentinians. this will take ships and fatigue the airframes over time all adding to the british military burden. and every little bit of effort the british exert somewhere else is less effort they can spend to annoy china.
and its pretty standard practice. every time china send even a single frigate into the sea of japan, the japanese surveillance planes scramble and they assign at least one ship to follow, every time a single russian bear bomber goes around the british islands, nato escorts them.
that single frigate has no chance of invading japan or even doing a whole lot of damage nor does a single bear bomber pose much of a threat(yes i know they can be nuclear armed, but regardless that single bomber isnt going survive british defenses) but japan still cannot allow it to roam freely and un-tracked just as nato must escort the russian bomber.
a few potentially unfriendly ships around means they'll have to have their ships follow, stretching their already limited fleet, a few jets flying near the airspace means those Eurofighters will be spent all the quicker. all this is good for china, especially since china isnt even paying for it, it's in fact profiting from the sales, literally no down side for china.
You forget one thing - the Falklands are 600km away from the nearest Argentine air base and so if the Argentines want to send their JF-17s on such long round trips, then they would wear out their JF-17s far faster than the Eurofighters that are actually based on the islands as they all lie within a 100km radius of the centre of the archipelago.
The Falklands does not even add to the stress of the UK airframes as those Eurofighters would need to anyway fly regularly and it makes an ideal location to practice low and fast flying over large uninhabited areas that is almost impossible to find in the UK.