Unlikely. I've worked as a delivery driver for a couple of different places and it was always W2. If you're scheduled to work and you deliver only for Instacart, the IRS will almost certainly view you as an employee.
Uber and Lyft both 1099 their drivers. I'm not sure specifically about Instacart but I imagine most "on-demand" companies that can get away with it, will do it.
If they're having you use your own vehicle and not forcing you to adhere to a specific schedule, they can probably do it.