Oui, c’est tout à fait vrai. Au début du XIV^e siècle, par exemple, au jour d’ui signifie « le jour où l’on est ». Puis ui est devenu hui et aujourd’hui est devenu un mot (après un passage par aujourdui à la fin du XIV^e siècle).

Ceci est expliqué avec plus de détails ici (voir section “ÉTYMOL. ET HIST.” en fin de page).

This is expounded in R.L. Trask, Robert McColl Millar’s Why Do Languages Change? (2010 Rev. ed). p. 24 Bottom

  In early Latin, ‘today’ was expressed by the phrase *hoc die, literally ‘on this
day’, where the asterisk shows that this form is not recorded but has been

p. 25

reconstructed by linguists. By the time of Classical Latin, this phrase had
coalesced into a single word, hodie, with the loss of one consonant in the
process.
  By the time of the first Roman emperor, no Latin speaker was pronouncing
aitches any more. Hodie was now being pronounced odie, even though educated
people kept on writing the aitches because of the prestige of earlier writers.
  In Paris, there were further changes in pronunciation, and in particular
more sounds were lost. In hodie, the sound /d/ disappeared, and after a while
speakers of the Parisian variety of Latin, which was beginning to be called
‘French’, were writing their word for ‘today’ as hui, though that was only
an act of obeisance to the ‘mother’ language, and what people were really
saying could have been written ui.
  It appears that speakers of French were getting a little uncomfortable uttering
such a small noise to say ‘today’. So, they responded by creating a more
substantial way of expressing that concept. What they came up with was the
orotund phrase au jour d’hui, which is literally ‘on the day of today’. This
certainly solved the problem, and people began using this heavy expression
more and more often, until finally nobody was saying just plain hui any more at
all. Today the only possible way of saying ‘today’ in French is aujourd’hui,
which is now written as a single word, and the former hui is dead and buried.
Almost inevitably, this word can be reduced to something like dwee in colloquial speech.
  Very likely you know somebody who is constitutionally incapable of uttering
the little English word now and who replaces it on every occasion with the
mouth-filling sequence at this moment in time. So far, this remains a pompous
piece of bureaucrat-speak, inveighed against by usage handbooks everywhere,
but there is no guarantee that it will not one day displace its shorter equivalent
altogether, much as has happened in French.

Hui comme dans huis clos (portes closes) veut dire porte au singulier en vieux français, ainsi aujourd’hui veut dire “à la porte de ce jour”