[Lev 19:27 ESV] (27) You shall not round off the hair on your temples or mar the edges of your beard.
Related article from Jewish Encylopedia.
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Most likely not.
The passage we find this commandment in is as follows (my translation):
... I, the Lord, am your God.
You shall not eat anything in its blood,*nor do incantations, nor anything arcane.
You shall not shave around the sides of your head, nor tamper with the sides of your beard.
And you shall not make in your flesh any cutting for the dead, nor mark any writing upon yourselves: I am the Lord.
* Somewhat obscure: לא תאכלו על הדם ("you shall not eat against/upon/in/with blood")
Translation-wise, I think "round the edges of your head" is too rigid and non-contextual a translation or interpretation. Edges hear seems to refer to the sides, i.e. "around the head."
The whole little pericope seems to have to do with pagan practices (cutting onself for the dead, making markings in their flesh, divining etc.), ones to be avoided by Israelites. A sign for setting them apart, I don't think, is in view at all except in that they are not to do what makes one pagan—which here clearly refers to cultic cuttings and shavings, not keeping your hair and beard trimmed. It seems to have the same thrust as the following (Deuteronomy 14:1-2):
You are the children of the Lord, your God: you shall not lash yourselves or make a baldness between your eyes for the dead. For you are a holy people to the Lord, and the Lord chose you to be His for his own people over all the peoples upon the face of the earth.
The Hassidic practice seems to be a novelty, and is entirely absent from art depicting Jews, by Jews, from ancient times.
The following fresco from the Dura-Europos Synagogue (second century) is representative of ancient Jewish art.
(David is anointed by Saul).
Here, none of the males have long sidelocks, or even beards for that matter (on most of them).
Later, even from art from a the 6th century Synagogue in Gaza, again, we have King David sporting a baby-smooth face, and no sidelocks—or beard:
This is inconceivable if this was in any way the ancient and indispensable practice of the Jews. It seems like yet another one of the result of the kind of pedantic surmising discussions found in the Talmud, and for to tire an old trope, a 'tradition of men.'