I do not think it should be interpreted in that way, though the traditional translators did not provide any alternative meaning to that phrase draviḍaśiśur.
तव स्तन्यं मन्ये धरणिधरकन्ये हृदयतः
पयःपारावारः परिवहति सारस्वतमिव ।
दयावत्या दत्तं द्रविडशिशुरास्वाद्य तव यत्
कवीनां प्रौढानामजनि कमनीयः कवयिता ॥ ७५॥
O Daughter of the Mountain-King! I fancy that Thy breast milk is the milk-ocean emerging as poetic inspiration from Thy heart. For, it was by drinking it, so graciously given by Thee, that the the draviḍaśiśur became a noted poet among great composers.
——-
As far as I understood, we should not consider a single word or a phrase alone, while trying to understand the intricate meaning of the shloka composed by a towering personality like Shri Adi Shankara.
If we consider the entire 2nd line, we can find that the meaning will be as follows;
दयावत्या दत्तं द्रविडशिशुरास्वाद्य तव यत्
कवीनां प्रौढानामजनि कमनीयः कवयिता ॥
For, it was by drinking it, so graciously given by Thee, that the draviḍaśiśur became a noted poet among great composers.
——
I have kept the phrase as it is, so that we can concentrate on the meaning of the remaining part, from which we can try to deduce the meaning of the phrase draviḍaśiśur.
The composer was saying that by drinking the the DIVINE milk of Parvati, he had become a famous poet among great composers.
Now, a question arises as to how a child coming from a particular land area can become a famous poet among great composers, by drinking the the DIVINE milk of Parvati?
To me, it is not properly fitting into the meaning of rest of the shloka.
There is another meaning to द्रविड - group of grammarians
The literal meaning of draviḍaśiśur can be an amateur among grammarians.
The esoteric meaning of draviḍaśiśur can be a person, who is an infant among poets.
If we replace this meaning for draviḍaśiśur, we can get a different meaning.
——
दयावत्या दत्तं द्रविडशिशुरास्वाद्य तव यत्
कवीनां प्रौढानामजनि कमनीयः कवयिता ॥
For, it was by drinking it, so graciously given by Thee, that myself, an infant among poets, became a noted poet among great composers.
