Here's what I've concluded.
The front desk has to manually assign up to two drivers per room access to the parking garage. If you have 1 or 2 adults on your reservation and you complete online check-in, there's a chance the front desk will do this for you ahead of time, and your bands will work to access the gate right from the beginning without stopping at the desk first.
However, if you have more than two adults on your reservation, the front desk will not assign anyone parking access ahead of time because they need to you tell them which two adults you want to have access to the garage as drivers.
So if you have 1 or 2 adults, your bands MIGHT work the first time. If you have 3+ adults, they definitely will not.
Note that this doesn't really have anything to do with MagicBands. You could bring an old Walt Disney World room key or park ticket, anything assigned to your My Disney Experience profile, and it will work exactly the same way.
Finally, I don't think any of this matters for a newbie because I would never recommend going to the self-parking lot for your first time anyways. You want to make the grand entrance through the lobby doors, not scurry through the back entrance in the parking garage.