I don't know exactly what +Williamson has to say, but I do know that in the past, both he and +Lefebvre said the NO ordination of at least one priest, Fr. Hesse, was valid.
In one of his talks posted on YouTube, Fr. Hesse is quoted as saying: "...I have been ordained, unfortunately in the New Rite of Ordination, but thank God in Latin, everything strictly by the book and +ABL said that would be valid, +Fellay said it's valid and Fr. Franz Schmidberger who is my present superior in Austria says it's valid and +Williamson said there's no need for conditional ordination...."
In previous discussion on the matter, I called the SSPX and posted what the man told me here.
Read Chapter 15 in Who Shall Ascend? (also attached below) where Fr. Wathen touches on the subject, here is a snip....
"...It is not our purpose in these pages to decide whether the new ordination rite is invalid, though, as we shall see, the argument is substantial enough that we are bound to allow for this possibility. Furthermore, we must see the issue in the context of the total redefinition and reconstitution of the Church, such as was set in motion at the Council. In view of the fact that, since the Council, the priest's role has been in the process of being modified, as we said, to that of a Protestant presbyter, there is every reason to deduce that the new ordination rite sabotages the Sacrament of Holy Orders according to
the explicit program and purposes of those now in power. (The reader is reminded that the very doubt which this change creates serves the malevolent purposes of the conspirators as well as does the certitude of invalidity, because from the doubt flows controversy, disagreements, factions, confusion, and disquietude among the clergy and the faithful.)..."
Very good information above. I agree with the highlighted text above from Fr. Wathen, in that he states that the doubt which the change creates serves the purposes of the malevolent conspirators (who are the Modernists, I take it), but that the certitude of invalidity also causes controversy, disagreements, factions, confusion, disquietude among the clergy and faithful.
Sedevacantists, IMO, in particular tend to view the new sacraments as invalid, since they are no strangers to controversy. But it's not only Sedes of course who say that the New Rite is invalid.
If I recall correctly, Fr. Hesse maintained that the New Rite of Consecration is valid, and he gave the reasons for this stance in one of his talks, which I cannot now find with an internet search. But his reasoning made sense. Of course, the New Rite of consecration may not be administered properly, due to the essential role of the priest being changed of course, as has been explained already. +ABL did not always re-ordain the priests who defected from the Novus Ordo to the SSPX. Therefore, it stands to reason that it isn't the words of consecration that are the problem, but rather how it is administered, or if the words are changed.