Great question… a real world situation from someone doing their best to follow the law but also be realistic about time/distance. What follows is my opinion on the matter based on lots of electric bike riding experience, this is not legal advice. You can probably ride with electric assist across the dirt way with no issues and avoid any negative response that might arise as long as you’re polite to other cyclists and pedestrians and pedal along without going too fast. If someone called you out about it you could easily hop off, walk your bike and explain that you use the assist to help make your commute possible or possibly, like me, you have a knee injury and it’s difficult to pedal through softer terrain like gravel. Another different approach might be to shut the bike off completely before entering the gravel section, you could even take the battery off and put it in a backpack or as mentioned earlier… just walk the bike. Imagine if you had a motorized dirt bike and were just pushing it along a sidewalk… this kind of vehicle definitely is not allowed on sidewalks or most gravel paths like the one you’re describing but if you were escorting it carefully, you’d be honoring the spirit of the law and if an officer or pedestrian jumped out and started questioning you about your “motorized vehicle” it is my feeling that a genuine explanation and apology or request for guidance would go very well. I personally have never had issues riding electric bikes in part because I am thoughtful about how I use them. I do occasionally switch them off and sometimes I get off and walk. I have asked police in many cities across the US what they thought about ebikes and in every case I have received positive interest and support with guidance to ride safe with a helmet and follow traffic laws in the street. I hope this helps and I wish you well, it’s nice that you care enough to ask and I hope you’re treated well by others out on the road. The flip side of this response is that I have been harassed, yelled at and even swerved at by automobiles when riding bicycles and electric bikes. This usually happens in the evening after work lets out when traffic is heavy and I’m riding on the shoulder or in the street (where marked to do so) and I believe it has to do with territory, testosterone and socio-economic standing more so than laws or anything like that.
Some power-on-demand only e-bikes can hardly be confused with, let alone categorised as, bicycles. For example, the Noped is a term used by the Ministry of Transportation of Ontario for e-bikes which do not have pedals or in which the pedals have been removed from their motorised bicycle. These are better categorised as electric mopeds or electric motorcycles.
Many newer or smaller companies only design and market their products; the actual production is done by Asian companies. For example, some 60% of the world's bicycles are now being made in China. Despite this shift in production, as nations such as China and India become more wealthy, their own use of bicycles has declined due to the increasing affordability of cars and motorcycles. One of the major reasons for the proliferation of Chinese-made bicycles in foreign markets is the lower cost of labor in China.
You turn it on by pressing the green button on the battery once for low power and twice for high, although to be honest, there is not a lot of difference between them. After that, you just pedal. There are no gears, no chain to muck up your trousers (a motorbike-style carbon fibre belt is used instead) and not that much difference in feeling compared to riding a normal bike.
The Class 3 Aventon Pace 500 urban e-bike has five levels of pedal assist and tops out at 28 mph. But the Pace has something not found on a lot of modern e-bikes. In addition to pedal power, it also has a throttle—in the case of the Pace, a small thumb paddle on the left side of the handlebar next to the control unit that holds at a steady 20 mph, no pedaling required. The bike itself has an aluminum frame, a swept-back handlebar, ergo grips, a sturdy kickstand, hydraulic disc brakes, 8-speed Shimano Altus shifting and gearing, 27.5x2.2-inch Kenda e-bike-rated tires, a saddle the size of Texas, and good ol’ classic city/commuter-bike geometry. It doesn’t come equipped with fenders or a rear rack, but you can add them. Power comes in the form of a 500-watt rear-hub motor, a semi-integrated battery on the down tube (with a range of up to 50 miles), and a backlit display unit mounted on the stem.
Oklahoma the following restrictions on the operation of Electric-Assisted Bicycle in 47 O.S. 11-805.2  as follows: 1. Possess a Class A, B, C or D license, but shall be exempt from a motorcycle endorsement; 2. Not be subject to motor vehicle liability insurance requirements only as they pertain to the operation of electric-assisted bicycles; 3. Be authorized to operate an electric-assisted bicycle wherever bicycles are authorized to be operated; 4. Be prohibited from operating an electric-assisted bicycle wherever bicycles are prohibited from operating; and 5. Wear a properly fitted and fastened bicycle helmet which meets the standards of the American National Standards Institute or the Snell Memorial Foundation Standards for protective headgear for use in bicycling, provided such operator is eighteen (18) years of age or less.
On the other hand, the battery doesn’t lock into the bike, which means you can’t just leave it on your bike when you park at the bike rack. Anyone could walk by and simply remove your battery. That seems like an oversight to me, though perhaps the designers assumed that such a small battery would just be easy to take with you. And it is. My wife could probably lose this battery in her purse.