Beating eggs & sugar when making gelato
No, it doesn't have to thicken, at least not in the way custards like creme caramel thicken. "Coat the back of the spoon" is just a misnomer, a term known to experienced cooks which confuses everybody who learns to cook on their own. 

For "Coat the back of the spoon", read the comment riotburn left at the question What is the correct consistency of a cream soup?. It says: "The best way to describe 'coat the back of a spoon' is where if you dipped the spoon into the soup, take it out and holder over the pot, you'll find thin film (&lt;1mm thick)."

For the ice cream, heat to between 80 and 85°C. I've explained it somewhere else, but in short, this gives you enough thickening without overcooking. If it is really gelato and not French style, it should be thickened with starch anyway. Also, watch videos on the Internet for how to make ice cream, they show the correct consistency. I think Allrecipes had a good one, but their search is so strange, I can't find it and don't know if they have it or not.