Well no, Sqad. The only places you could touch were your own sides. There are many theories as to why this style of dancing developed.
The Catholic Church considered moving the arms was flirting. Priests monitored the dancing.
Irish pubs are so crowded that there was no room to move the arms when dancing.
When the English invaded Ireland and looked out of their windows at the Irish dancing they could only see the top half of the dancer. It then looked to the English that the Irish were jumping for joy at the presence of the invaders.... :-)