Is there any connection, etymological or other, to the Greek fertility god Priapus?

AS-- Do you mean with ithyphallic? Well, there's no accepted etymology for Priapos the ithyphallic god of fertility and gardens. So, I guess, no. Chantraine (who wrote a comprehensive Greek etymological dictionary) says "Pas d'etymologie." He also suggests that Priapos was imported, like many another Greek god, from Asia Minor. I saw a great Priapus in Pompey back in '76. The guard, for a small pour-bois, would unlock a little door behind which was a little statue of the god with his member erect and slightly longer than he was tall. (Luckily for me, the two little old ladies from the Midwest in front of me paid, so I tailgated in on their tip.) According to archeologists they were common in Roman gardens and acted as scarecrows. (I think Horace mentions one of these statues of wood cracking and making quite a noise.) We get the word priapism a medical condition 'persistent and usually painful erection'. Some great words in Greek are: priapiskos 'dilator or suuppository (for the anus); perineal peg; plug (for the nose)', priapiskotes 'shaped like the membrum virile', and priapistai 'worshippers of Priapos'. The Romans, not to be left behind, have priapus vitreus 'a drinking vessel of obscene shape', and priapus siligenius 'a cake of the same shape'. I've seen items that could be their modern descendents. Not sure what they're called.

Another great book for the wordhoarder is J N Adams, The Latin Sexual Vocabulary. Full of all kinds of great dirty words and a good stocking stuffer (Freud forfend!) for any budding classicist.