The SSPX explicitly recognizes both the Pope and all Dogmas of the Church, including the Vatican I declaration regards Papal Infallibility.
See http://www.catholicherald.co.uk/news/2012/07/19/sspx-we-recognise-the-authority-of-the-pope/
Those who want to have the Catholic Caucus include sedevacantists must use the term "Catholic/SSPX Caucus." And if they wish to include Orthodox as well, they must stipulate "Catholic/SSPX/Orthodox Caucus" or "Catholic/Orthodox Caucus" as the case may be.