I will compare two Church Histories on this point. The first is J.E. Darras’ 4 volume book, “A General History of the Catholic Church.” The other is Philip Hughes’ 3 volume book, “History of the Church.” In Volume 3 Chapter 3 Section 1 Part 5, Darras says: Urban made a last effort; he offered to lay the validity of his claim before a general council. [The Cardinals’] refusal of this proposal will ever remain an indelible stain upon their memory. Urban then created twenty-six new cardinals to fill the places left vacant by the seceders…[but] never once resorted to the spiritual weapons at his command, while the cardinals flooded the world with copies of a manifesto, in which they abused the Pope as an apostate and an intruder. Then, in Parts 8-9 of this section, a few pages later, Darras says: From Rome and Avignon, their respective residences, the two Pontiffs launched their anathemas against each other. Philip Hughes’ book is more summary. In Volume 3 Chapter 3 Section 4 Part 1 he says: [The Cardinals] went into conclave [again], and at the first ballot they chose as pope Robert of Geneva. He called himself Clement VII. … For the next nine months the rival popes confronted each other in Italy, separated by a mere sixty miles and their own armed forces. Urban, on November 29, excommunicated Clement and some of his chief supporters. Since Clement VII was excommunicated, it would seem impossible for him to have become pope upon the death of Urban VI, as previous antipopes had done. Therefore, the only successor the pope could have had, it seems to me, is the one who was elected by the Cardinals whom Urban VI had appointed, and they elected Boniface IX.
Not necessarily. A person is known as the Bishop of Rome (and thus Pope) by a consensus of the Catholic Church, regardless of his manner of his election.
Do you have a citation for that? I am inclined to doubt it for several reasons. One is, Canon Law tells us how the election of a pontiff is to proceed, and the consensus of the Church seems to have nothing to do with it. It seems to me that the decision of the Cardinals meeting together in a consistory is what counts, and the lawful pope, Urban VI, seems to have appointed sufficient cardinals to elect his successor even without the ones in league with the antipope (and excommunicant) Clement VII.