Daniel Becker, Patent Attorney and Early-stage Engineering (2013-present)
It depends on the vehicle, but, in 1st gear, at 1000 rpm, it is hard to imagine that you are going very quickly!
If I understand your question correctly, then the answer is no. Driving at a crawl, essentially just barely pulling away from a complete stop, is not efficient. An internal combustion engine (particularly a reciprocating piston-cylinder engine) is a device which, relatively speaking, has a narrow range at which it produces the most force per unit fuel. This quantity is known as brake-specific-fuel-consumption (BSFC).
In an engine designed to maximize BSFC under its most frequent operating conditions, it is designed to suck-in and blow-out air at an engine speed which is correlated with a common crusing speed by the gears in the transmission. For example, driving in 4th gear at 40 miles per hour is probably a good, frequent city condition. Another would be 5th or 6th gear at 55 mph. In each of these, the engine speed will be scaled so that the engine runs at a speed at which air moves into and out of the cylinders at a rate which optimizes completeness of the entire combustion of fuel injected, minimizes heat loss, and best translates the combustion force into rotating force with the least resistance. All of these design characteristics are selected before almost any other engine component is developed.
By comparison, 1st gear is not for continuous driving. It is useful for maximum wheel torque, which is valuable for climbing hills, initiating rolling away from a stop, and accelerating the car up to the slightly higher speeds at which the engine can develop the torque necessary to move the car with significantly less leverage (2nd and 3rd gears). This very very short gearing is selected so that the engine can be nudged into a high-torque level very quickly, so that it does not have to stay in that range. At low vehicle speeds, heat accumulates, engine energy is used to drive cooling accessories but the output torque is very small, so there is a small margin for exceeding its base loads, and it is generally very inefficient.
With cars idling at 800–1000 rpm, driving in 1st gear is barely more efficient, in terms of engine efficiency, and only manages to improve upon idling by the car making SOME rolling progress, as opposed to a complete stop. This is why so many cars have stop-start idling systems now.
Did that answer your question?