Question
How come Shukadeva did not undergo Upanayanam?
Answer
First of all, the Madhwa commentator Viijayadhvaja Tirtha and the Pushtimarga Acharya Vallabhacharya both say that the word "pravrajantam" in this verse does not mean taking up Sanyasa, and that Shuka did not take Sanyasa without doing Upanayana; see page 15 of this book. Second of all, the Sri Vaishnava Acharya Vedanta Desikan actually discusses Shuka in this excerpt from the Alepakamatabhangavada, a chapter of his Satadhusani devoted to refuting the Advaita view that those who have attained Brahmajnana do not have to follow the rules of Varnashrama Dharma.
The Advaita opponent cites Shuka as an example of someone who didn't follow Varnashrama Dharma because he had Brahmajnana. Here is how Vedanta Desikan responds:
[Opponent:] "Since the authoritative texts disclose that Ribhu, Shuka, Samvarta and the like practised nudity and other similar vows, we believe that they were outside all the ashramas." [Response:] That is not true, because even nudity is a special kind of vow that aims at enduring rain, wind, heat, and the like; a vow that is associated with the special practice of eating each mouthful completely (as soon as it is received). It is a vow that only certain unique men of ancient times were qualified to perform. If he were outside the ashramas, how could the king have chosen Samvarta, who was subsisting on air alone, as the priest for his sacrifice? Nudity, therefore, is just a special vow common to all varnas and ashramas, for only householders can perform priestly functions and the like. In the olden days even a widower, after fulfilling certain conditions such as taking a (new) wife, was considered fit to function as a priest.
[Opponent:] "'Over five hundred royal courtesans flocked to him.... After he had eaten, my dear, each of them in turn showed him the beautiful park of the female quarters in the palace.' [Mahabharata 12.312.37,39] Surely, these texts show that the great seer, Shuka, a knower of Brahman, also ate in the company of courtesans." [Response:] Wrong, because that statement is also made with reference to a situation in which these women were employed as servants to feed Brahmins and others who had completed their Vedic initiation, and, after the meal, to perform such services as fanning. It is quite clear that the intent here, indeed, was only to test Shuka's chastity and other such virtues. The text does not indicate that he ate forbidden food....
In the following passage of the Bhagavata Purana describing the appearance of the Paramahamsa Shuka, moreover, the phrase "he had no visible emblem" is used to indicate the concealment of the emblem, because such concealment is associated with the vow of nudity: [...] "He had the appearance of an Avadhuta, he had no visible emblem, and he was surrounded by children." [Srimad Bhagavatam 1.19.25]
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