So let's assume we wanted to convert, say, 1/9th the mass of Ceres into cars. Now, Ceres is pretty much at the minimum mass for a dwarf planet, although Vesta is also pretty large for an asteroid. Let's assume that the "small dwarf planet" Orion mentions is 1/9th the mass of Ceres but is much more metal-rich and thus has a higher surface gravity. Just for the sake of calculations.
Now, the energy needed to manufacture an average car is around
73 gigajoules (if my source is correct). Let's treat this as a low-end, since we are talking sophisticated drones rather than cars. The average car is 2 tons, so we put that into google to get 72 gigajoules / 2 tons so far.
Now, the mass of our planetoid would be 1e20 kg. Multiply our google entry by this, and divide by the total energy that Earth receives from the sun aaaaand...
We get 1045 years. This is if you covered the whole Earth in 100% efficient solar panels. That's a Preposterous Amount of Energy™, and would equate to about 4.25 × 10^17 watts. But assuming they do have a source of energy like this, the total amount of energy harvested would be enough to heat 10 Ceres' worth of water by about 700°C, but we've established we are talking about a much larger planetoid. I've done the calcs myself for an order-of-magnitude guess at the properties of this secret source, but I don't exactly want to explain it since, well, plot.
Don't take this as an actual indication of the capabilities Orion is talking about (if he isn't lying/wrong), just a rough thought experiment for fun.
Also, the Earth receives enough solar heat to build 2.4 million cars per second.