In my experience with a canister ice cream maker, it doesn't matter how you get the custard down to just above freezing, as long as you make sure to do so before you put the custard in the canister. Especially on a hot summer day.
I usually just put the custard straight into the freezer and give it a stir every five minutes until it tastes cold. One time the phone rang and I forgot about a blueberry sorbet mix for a lot longer. When I remembered it, it was a lot harder to stir, and there were a small number of ice crystals. I ended up just leaving it in the freezer and stirring it another couple of times before serving it. It was chewy rather than fluffy, but quite tasty.