To the best of my knowledge, they have not.
A Byzantine Catholic priest nearby has stated that they do not accept the teachings of Vatican I. I mentioned this to catholicguy once and he said the priest didn't sound very [Roman] Catholic to him. Being faced with a situation where the priest is claiming obedience to the Pope but rejecting (at least) some of the Western councils, I believe catholicguy was correct but I truly don't know what to make of it all.
All that proves is that we still have, as usual, heretics in the Church.
Old Catholics The sect organised in German-speaking countries to combat the dogma of Papal Infallibility.
Filled with ideas of ecclesiastical Liberalism and rejecting the Christian spirit of submission to the teachings of the Church, nearly 1400 Germans issued, in September, 1870, a declaration in which they repudiated the dogma of Infallibility "as an innovation contrary to the traditional faith of the Church". They were encouraged by large numbers of scholars, politicians, and statesmen, and were acclaimed by the Liberal press of the whole world. The break with the Church began with this declaration, which was put forth notwithstanding the fact that the majority of the German bishops issued, at Fulda on 30 August, a common pastoral letter in support of the dogma. It was not until 10 April, 1871, that Bishop Hefele of Rotterdam issued a letter concerning the dogma to his clergy. By the end of 1870 all the Austrian and Swiss bishops had done the same.
The movement against the dogma was carried on with such energy that the first Old Catholic Congress was able to meet at Munich, 22-24 September, 1871. Before this, however, the Archbishop of Munich had excommunicated Döllinger on 17 April 1871, and later also Friedrich. The congress was attended by over 300 delegates from Germany, Austria, and Switzerland, besides friends from Holland, France, Spain, Brazil, Ireland, and the representatives of the Anglican Church, with German and American Protestants. The moving spirit in this and all later assemblies for organization was Johann Friedrich von Schulte, the professor of dogma at Prague. Von Schulte summed up the results of the congress as follows:
Adherence to the ancient Catholic faith;
maintenance of the rights of Catholics as such; rejection of the new dogmas,
adherence to the constitutions of the ancient Church with repudiation of every dogma of faith not in harmony with the actual consciousness of the Church;
reform of the Church with constitutional participation of the laity;
preparation of the way for reunion of the Christian confessions;
reform of the training and position of the clergy;
adherence to the State against the attacks of Ultramontanism;
rejection of the Society of Jesus;
solemn assertion of the claims of Catholics as such to the real property of the Church and to the title to it.