Probably just as much unity as there was in the church at the time of the beginning of the Reformation without it. And I would hope that you won't tell me there is unity in the RCC today. I can just read the headlines to know better.
Doctrinal unity, absolutely. There is a range of authority regarding Church teaching, however, ranging from "De Fide" dogma which must be believed by all Catholics through the more difficult to discern authoritatively "ordinary Magisterium" through theological consensus, speculation and opinion.
Ott outlines the various levels of certainty regarding Church teaching in descending order:
1) De Fide- Divinely revealed truths (infallible)
2) Church Doctrines (as infallible as above)
3) Teaching proximate to faith - generally regarded by theologians as a truth of Revelation but not yet formally promulgated by the Church.
4) Teaching pertaining to the faith - theological teaching whose truth is guaranteed by its intrinsic connection with the doctrine of revelation (theological conclusions) but not yet promulgated by the church.
5) Common teaching.
6) Theological opinion.