No, our being in communion with each other derives from receiving Our Lord in the Eucharist and not from holding hands. People blame this on Protestants but plenty of Protestants don't hold hands with at their services.
Folks complain that drinking from the chalice or receiving on the tongue is unsanitary but don't complain that shaking hands at the sign of peace of holding hands at the Our Father is...even though people touch their faces, blow their noses, and Lord knows what else without washing their hands, right before receiving Communion in the hand.
Some people are shy and don't want to hold hands with people they don't know (hand holding is rather intimate). Don't folks who decry rape culture say that people who don't want to be touched shouldn't be forced to have others touch them without their consent? Sometimes the priest tells the congregation to hold hands. Perhaps we can kneel instead?
Lots of hugs/handshakes at my EF parish, before/after but never during the Mass.