Oh goody, we are getting deeper and deeper into areas of my expertise ! LOL
I took four years of Latin, and though YOU have attributed harry to a Latin precursor, this is NOT the truth. The word is a direct descendent of and is rooted in the ancient Germanic / Tuetonic . As you no doubt know, this ancertral tonuge is far removed from Latin, and isn't part of the " Romance " languages, which derive from Latin.
How far back would you like to trace the modern theatre from ? Primative society ? Shall we start with the Greeks; as they are an easier jumping off point. There are NO devils in Greek tradgedies or comedies. There are witches; but no wizards. Ancient Rome borrowed much from Greek theatre, though, truth be told, their comedy and farce are the true precursors of Punch & Judy, Mystery / Passion plays, The Commdia Dell'Arte , and modern theatre ; including Vaudeville, Burlesque, and The English Music Hall.
Punch and Judy shows, predate the Commedia Dell'Arte ( from whence the Harleqin character comes from ), and is just the sort of play, that the earliest Passion or Myster plays , from the mid 5th century A.D. , were used to reinforce Biblical / allegorical concepts. Yes, the devil plays a role in both , and is prominent in Punch and Judy. No, he is NOT called " HARRY ", in any versions.
Masks have been used, in plays, from time immimorial; from priative societies, through the ancient Greek, Roman, tribal English / French Mummer ( which are, in fact derived from the pagan rites of May day, or Beltane. The Geeks used them to not only serve the purpose that makeup now does, but also as the FIRST audio system. You see, they were constructed to amplify the voice, like megaphones do, pre today's microphones. There is just so far that the human voice, even when trained , can be thrown when talking. Yodelling or singing can extend the voice,over an even greater distance ; however, the actors didn't sing their parts. The ancient MUMMERS, worse masks, as part of the shaministic " magic " , of taking on ( changing into / shapeshifting ) the persona of the animal spirit , of the skis and masks they wore.
Alberto Naselli, probably the first Harleguin, would argue with you that this character is in any way a representative of Satan. Please state your source for such a nonhistorical claim. Almost every single character, in the Commedia Dell'Arte repitoire wore a mask , and NONE of them did so, because they were implying the devil. That was the form of this type of theatre , and as a matter of fact, Commedia Dell'Arte, is often called : " THE COMEDY OF MASKS".
Now, if you want to actually trace the Commedia Dell'Arte, to it's original roots, then we mst talk about the Zannis, which in turn, has its roots in ancient, pagan , Northern Italian folklore, with a connection to propriation rites and celebrations similar to the mdern carival. Yes, they were minor " demons " ; but , NOT Satan, the devil, etc.! This is your own assumption, and not born out by any authority on the threatre.
If you need help understanding this, in a fuller context, I shall be happy to walk you through it, via FREEPmail. :-)