There is no direct reference to that verse in Complete Works and that's because Swami Vivekananda did not agree that Shudras are forbidden to study the Vedas.
Complete Works / Volume 6 / Epistles - Second Series / VIII:
The Achârya(Adi Shankara) could not adduce any proof from the Vedas to the effect that
the Shudra should not study the Vedas. He only quotes ("The Shudra
is not conceived of as a performer of Yajna or Vedic sacrifices.") (Tai. Samhita, VII. i. 1)
To maintain that when he is not entitled to perform Yajnas, he has neither any
right to study the Upanishads and the like. But the same Acharya contends with
reference to , ("Now then commences hence the inquiry about
Brahman.") (Vedânta-Sutras, I. i. 1) that the word (Ath) here does not mean
"subsequent to the study of the Vedas", because it is contrary to proof that the
study of the Upanishad is not permissible without the previous study of the
Vedic Mantras and Brâhmanas and because there is no intrinsic sequence
between the Vedic Karma-kânda and Vedic Janâna-kânda. It is evident,
therefore, that one may attain to the knowledge of Brahman without having
studied the ceremonial parts of the Vedas. So if there is no sequence between
the sacrificial practices and Jnana, why does the Acharya contradict his own
statement when it is a case of the Shudras,by inserting the clause "by force of
the same logic"? Why should the Shudra not study the Upanishad?
Complete Works / Volume 4 / Writings: Prose / What we Believe in:
Who wrote the
Upanishads? Who was Râma? Who was Krishna? Who was Buddha? Who
were the Tirthankaras of the Jains? Whenever the Kshatriyas have preached
religion, they have given it to everybody; and whenever the Brahmins wrote
anything, they would deny all right to others. Read the Gitâ and the Sutras of
Vyâsa, or get someone to read them to you. In the Gita the way is laid open to
all men and women, to all caste and colour, but Vyasa tries to put meanings
upon the Vedas to cheat the poor Shudras. Is God a nervous fool like you that
the flow of His river of mercy would be dammed up by a piece of meat? If such
be He, His value is not a pie!
Complete Works / Volume 3 / Lectures from Colombo to Almora / My Plan of Campaign:
There
are books where you read such fierce words as these: "If the Shudra hears the
Vedas, fill his ears with molten lead, and if he remembers a line, cut his tongue
out. If he says to the Brahmin, 'You Brahmin', cut his tongue out". This is
diabolical old barbarism no doubt; that goes without saying; but do not blame
the law-givers, who simply record the customs of some section of the
community. Such devils sometimes arose among the ancients. There have been
devils everywhere more or less in all ages. Accordingly, you will find that later
on, this tone is modified a little, as for instance, "Do not disturb the Shudras,
but do not teach them higher things". Then gradually we find in other Smritis,
especially in those that have full power now, that if the Shudras imitate the
manners and customs of the Brahmins they do well, they ought to be
encouraged. Thus it is going on. I have no time to place before you all these
workings, nor how they can be traced in detail; but coming to plain facts, we
find that all the castes are to rise slowly and slowly.
As you can see, Swami Vivekananda was not of the view that Shudras are not eligible to study Vedas. He said even Adi Shankara couldn't find any such verse from Vedas which prohibits Shudras to study Vedas.