If you want them to be economically competitive, then yes.
The largest current expense is the driver salary, mostly due to the low quality of the working conditions and extended stays away from your "home." If you're still carting people around in the truck, then you will have a difficult time competing with large personnel and technology expenses.
What I'm trying to suggest is that a fully automated nation-wide delivery service is going to be exceptionally difficult and will take a long time.
This is mostly from the perspective of OTR/long-haul transportation. You'll likely see faster adoption on smaller scales such as in-city delivery services like grocery delivery and the like. It will blossom outward from there but it's still going to be a very long process.
The response would be to have people fixed at these scales/fuel stops/docks that handle what the driver would have been doing.
Loading and unloading the vehicle at docks will adjust to meet a happy medium. As you already mentioned the single biggest expense is the driver, eliminating that is key, everything else will adjust accordingly.
Do they?
The trucks don't need to automate 100% of tasks for initial implementation, the first ones will be driverless in-between cities (or driver-nap in-between cities) with manned fueling, loading docks, scales, etc.
This will require some changes, but I don't think it will be too much of an issue to move toward full-serve gasoline service in the interim.