Here is an excerpt from Llewellyn George's A to Z Horoscope Maker and Delineator (29th edition, 1973) that offers insight into the constellation's relationship to the sign Scorpio.

Scorpio

...Scorpio in Arabic and Syriac is Al Akrab, meaning wounding, conflict, war. In Coptic it is Isidis: attack of the enemy, oppression from deadly foes. Antares (Shiloh) was then the principal star in Scorpio meaning it tears, rends, cleaves. It also denotes ruptures, burstings, crevasses and falls. "Now this man purchased a field with the reward of his iniquity, and falling headlong, he burst asunder in the midst and all of his bowels (Virgo-Libra-Scorpio) gushed out." -- Acts 1, 18. (Speaking of Judas Iscariot, the disciple indicated by Scorpio.) It should be remembered that the constellations of old do not bear their same relations to the signs today, consequently, it does not mean that Scorpio people are Judases. While the scorpion and the serpent were in Scorpio, so also above them were Ophiuchus and Herakles, the former destroyers, the latter saviours, denoting the great heights to which Scorpio people can attain. Their surgical and healing ability is well known.

In the Hebrew Zodiac Scorpio was ascribed to Dan. Dan was "a serpent by the way (near the zodiac) and an adder in the path." (Path is the zodiac.) The serpent was evil or d-evil, or the destroyer. The banner of the tribe of Israel was originally a scorpion, but afterwards an eagle. Serpens, the serpent [is] in first decan.

Ophiuchus grasps the serpent firmly, and although one heel or foot is stung or hurt, the other crushes the scorpion's [sic] head. This is represented as Krishna in sculptured figures in one of the oldest existing pagodas in Hindustan. In some of the old Egyptian spheres the picture is that of a man enthroned, wearing the head of an eagle (the enemy of serpents) and given a Coptic name signifying "the chief who cometh." An Arabic word or name, AEsculapius, figures in the myths as a great physician and one of great achievements, and who though wounded was, nevertheless, raised to glory. ...

[NOTE: the following doesn't discuss Ophiuchus, but describes the evolution of the signs Virgo - Libra - Scorpio.]

Another point for interesting study: Virgo and Scorpio were originally one sign; Libra did not then exist, (notice the similarity between the signs [or glyphs of] Virgo and Scorpio) making but ten signs, namely: Aries, Taurus, Gemini, Cancer, Leo (Virgo-Scorpio) Sagittarius, Capricorn, Aquarius, Pisces. Much is made of the figures 1 and 0, indicating the generative principle in nature and the sex of male and female. This combination of signs in Virgo, the serpent woman or Angrogyne man ("male and female created He them") signified a garden (Virgo) with the tree (Libra) of life in the midst thereof, symbolized by a serpent (Scorpio) climbing the tree. But afterward the helpmeet (Libra as a room within a room) for Adam was created, that is Libra, the womb-man (woman). Libra was early indicated as a naked woman, hence the "fall" of man. The Sun has its fall in Libra; the fall of the year is in Libra. And the serpent (that which beguiles or leads astray) became the eighth sign, ruling the ninth, Novo or November, counting from Aries (March) as the first month. Thirty pieces of silver (Moon) correspond with the thirty days of a lunar month. (Synodical revolution). ...