No. The College Football Playoff crowns a champion and awards its trophy, and it is completely independent of the NCAA. The NCAA does not officially sanction it and still does not award or officially recognize a championship in FBS football.
The major polls and selectors (e.g. AP, AFCA, NFF/FWAA) also still independently crown a champion, but for all intents and purposes the CFP has now unified the titles. The NFF and FWAA joined together and have decided to automatically award the MacArthur Bowl trophy to the CFP champion. The AP and AFCA (i.e. Coaches' Poll) obviously risk losing credibility if they don't award their trophy to the CFP champion. The days of split champions is probably over, although in theory, and since 1869, anyone can name whatever national champion they want. The credibility of any particular selector or selection is a matter for debate. To settle matters of credibility, most sources turn to a historical list of "major" selectors that was compiled by some notable football historians and is published in the NCAA's official records book.
FYI, Pitt has 11 different seasons with championships coming from "major selectors" in the record book, but claims 9. Pitt essentially swaps the NCAA record book's listed 1910 Pitt title for SI's 1970 certification of Parke Davis' 1934 selection (since it used SI's certification consistently since 1970, well before the NCAA records book), and rightfully does not recognize 1980 and '81 which occurred well after the entrenchment of the two poll system in popular consciousness. Really, anything post 1950 (when the Coaches' poll started) that isn't AP, Coaches', FWAA, or NFF is really a shaky claim, although some schools to make claims based on other selectors. Before 1950, it gets murky, which is why people turn to the NCAA records book list of major selectors.