Long-term, yes.
What you need to remember about the British is that they always thought several steps ahead. In Europe, they didn't want to be invaded, which meant they didn't want potential launching ground Flanders in enemy hands, so they didn't want Flanders outflanked so they didn't want anyone being able to dominate Germany. In Asia, they didn't want India to revolt, so they wanted to be able to get troops there quickly, so they wanted to have control of Suez, so they wanted to control Egypt, so they didn't want Egypt lost, so they wanted to control the source of the Nile. Etc, etc.
So in this case, if they decide that Montevideo is a crucial strategic asset, they are going to be very concerned about even a notionally independent client state pointing a dagger at it just across the water. Especially when that client state is led by Catholics who could ally with France and/or Spain. Carmen de Patagones could potentially be attacked by land from Buenos Aires, meaning the Brits will want Buenos Aires. They might allow partial governance to the Portenos to get that, but they won't allow a territorial division. Of course, a revolt by Buenos Aires could cause the Brits to be kicked out of Montevideo too, but the circle has to be squared somehow.
The one part of OTL Argentina that could be excluded in the north. I could see the Brits feeling secure enough if they have a border around Cordoba and the salt flats.