Not always and I'd suspect that being a "Full-Service Shopper" (vs "In-Store Shopper") pays better so a large percentage are likely both preparer and deliverer.
Source: https://shoppers.instacart.com/
Source: https://shoppers.instacart.com/
Haven't worked as an ISS, but I presume that they have no say in their orders as they aren't paid per order. I actually have no idea if they even get a portion of tips.
source: have run for Instacart before.