Would bicycle chain oil provide enough lubrication and protection to components in an engine to allow it to maintain normal operation?
There are many different kinds of bicycle chain lube, but teflon based is the most common. These lubes are made for ambient temperatures, and would break down very, very quickly from the heat inside an internal combustion engine. They aren't used solely as lubricants, but to keep water, dirt, and grime away from the chain rollers so they don't bind and rust.
So no, you wouldn't get very far. I wouldn't put bicycle chain lube anywhere inside an internal combustion engine.
There are mineral oils markete d as being for bike use (3-in-1 for example) that would probably allow a sufficiently old car (i.e. designed to tolerate a wide range of oils) to run without completely ruining the engine immediately. But they're not much good in either situation -- much too light for an engine, and OK as a bike chain oil when invented for the purpose over 100 years ago, but things have moved on since then.
It does have uses on both cars and bikes -- but things like squeaky door hinges and bike gear shifters.
I'd say you're better off riding the bicycle to the auto parts store and buy the right oil.
Using the wrong stuff may work in a pinch, but short term convenience has to be balanced against the cost of decreasing the lifespan of the engine drastically.
I have Wet and Dry chain lubes. They both have volatile components to carry the lubricant into the rollers of a chain and then evaporate. Difference is a dry lube will turn try, whereas a wet lube retains some liquidity.
Upshot of that, your engine wants a permanent liquid lubricant so it can be pumped around by the oil pump. A dry lube would not work in a pump's impellor at all, and a wet lube would have too high a viscosity once the volatiles evaporate.
You'll also end up with a crank case with extra volatile gasses in it, generally considered a bad idea.
So in this case, the wrong oil just won't work. Spend the time to go get the right oil, and don't blow a $10k engine for an hour's "time saving"
No, no, no, a thousand times no (unless you lubricate your chain using motor oil, of course)!
There are two types of optimal bicycle chain oil. The first is based on Teflon and cannot be used in a car engine because it is not an oil, strictly speaking.
The second (and IMO best) bicycle chain oil is actually most commonly marketed as motorcycle chain oil. It's thixotropic, meaning when agitated it becomes extremely thin, probably too thin for car engine, and when it stands still, it becomes so thick the engine would damage itself upon starting.
Now, bicycle chain is not a high-tech application. You can lubricate your bicycle chains using motor oil. If your view of bicycle chain oil is that you use motor oil, then of course you can use the same lubricant for an engine too.
However, do note that motor oil is not the optimal chain oil for a bicycle. For those who like cleanliness, the Teflon based lubricants may be alluring, and for those who like durability and long application interval, the thixotropic motorcycle chain oils are the best.