It does.

Alfred Watson Hands , Coins of Magna Graecia: The Coinage of the Greek Colonies of Southern Italy pages 12-14
The mystic emblems, the Krateros and Distaff, appeared on the very early didrachms of the second period 473 B.C. but they did not influence the common types until the period of Archytas, 380 to 345, when the symbol, the kantharos, appears in the hand of the dolphin rider, and the rider himself appears no longer always in the athletic form of the son of the sea-god, but with the plump figure of Iacchus, the son of the wine-god Dionysus, the hero of the mysteries. For some time after this however the trident was a more common symbol. In the period of the Molossian Alexander 334-330 B.C. however, the plump child form appears with a flower-like topknot on his head, and a distaff with spirally twisted wool. These figures may be compared with that on a celebrated krater represented in the Archaeologische Zeitung (1850, taf. XVI) described by Gerhard, p. 161 seqq. The figures of Iacchus mark the great influence of the Chthonic mysteries upon the older national cults of Poseidon and Apollo. These plump little figures may be compared with the terra-cotta votive figures found in tombs at Tarentum, some of which are crowned with Bacchic ivy-leaves. Conf. Hellen. Jour. 1886. What did the distaff signify to the mint masters who placed it as a symbol in the hands of the figure of the founder in 530 B.C. ? From the fact that we see the kantharos in the hand of the founder on some coins and on others the distaff, and on others the distaff in one hand and the kantharos in the other, we naturally ask whether the distaff can be looked upon as a symbol of Dionysiac or Chthonic rites, or whether it has any associations with the mysteries.