Not an expert
But I think that a British success in capturing Buenos Aires might prove more counterproductive than beneficial. For one, extending control to the interior would be difficult, and I think that royalist forces in the area would still make life difficult for the British, often managing to cut off the city from the hinterland. It would be possible for the authorities of the viceroyalty to seek refuge to the interior (or Montevideo), as Xenophonte mentioned. It is possible that Montevideo, if it managed to remain outside British control, could supplant Buenos Aires to a large extent as the entrepot for Platine trade. Combined with the mistrust towards Britain, the anxieties about local defence running higher, and the weakening of the influence of the Buenos Aires (commercial) elites, it could mean that the loyalists could have perhaps a better chance to keep control of the viceroyalty's lands; if the British preferred Buenos Aires, the merchants and authorities at Montevideo would try perhaps to promote more trade with non-British subjects, such as Americans and Portuguese. On the other hand, without de Liniers' attempts to strong-arm Montevideo and terminate its privileges, the rift between the two primary cities of Rio de la Plata would probably not grow so large as IOTL, and, if the British presence turned out to be rather problematic or damaging to local economic interests, Buenos Aires elites could turn perhaps to Montevideo in order to collaborate and oust the British.
Another development is that the British could be encouraged by this success to try to attack other ports - Caracas, Veracruz and Havana in particular. In the case of Veracruz, were such an operation to succeed, it could perhaps affect mercury imports negatively, thus exerting further pressure on the mining industry - a development which neither the controlling interests, nor the merchants, nor those occupied in the mines would find positive; again, we could see perhaps an increase in trade with third parties, through previously secondary ports, as well as more distrust towards the British government.
Furthermore, news of the British success(es) could make the French authorities even more concerned about the flow of silver from the Spanish colonies, and more convinced of the "ineptitude" of the Spanish government. At the same time, opposition to Charles IV and the Prince of the Peace would become even stronger, resulting perhaps in earlier attempts to remove Godoy from his position of influence and perhaps even place Ferdinand on the throne. If this happened while Napoleon was still in East Prussia, the French might be unable to respond to a regime change in Spain in an effective manner, which could compel Napoleon to tolerate the new government in Madrid for the time being. I think that under these circumstances, realignment with Britain against France would be more difficult to entertain as an idea (therefore Napoleon could believe perhaps that the coup was to some extent in his favour, because it could result to more dynamic Spanish reaction to British actions), so I am not entirely sure about the actions of Ferdinand, apart from dismantling the network Godoy had built since the 1790s. Personally at least, I think he would stick to the policy of strengtening royal control, reform, and centralisation, and without a French invasion and the question of the afrancesados yet, a relative continuity in the administrative apparatus and the commitment to reform would provide for greater stability.
More speculative: but the combination of more successful British attacks against Spanish territories and the likely consequent economic repercussions might make local elites more worried about severing ties with Spain - and France. In my view at least, the failure of local forces to repel British attacks and the dislocations that could follow could make local merchants, landowners etc more careful about not rocking the boat. Combined with a more stable political situation in Spain, it could perhaps take some steam off the drive for greater autonomy