Only if you're going to "no true Scotsman" ice cream. For anyone not subscribing to that view, ice cream can be made with or without eggs. French style, Philadelphia style, Gelato, and churnless all differ in whether there are egg whites, egg yolks, cooked bases, and density.
One recent method is to use a Pacojet to take a hard-frozen solid block and turn it into ice cream.
The actual "cream" is thought to have been invented by Buontalenti:
https://en.wikipedia.org/wiki/Bernardo_Buontalenti
(eggs are needed to make "real" ice-cream):
https://www.florenceinferno.com/the-invention-of-ice-cream-i...