I don't like the "it depends" answers but that is unfortunately the case here. This seemingly simple scenario actually opens up a huge field of possibilities.
If the disclosure is in itself makes the invention clear to a person skilled in the art the patent is valid even though an experimental verification has not been undertaken. This is often the case for mechanical inventions. The side effect is unfortunately that many will find it obvious in view of the description itself and disagree with the patent being granted. Where the description itself is not sufficiently convincing such as an improved escapement for a clock or pharmaceutical inventions.
> I assume that if it turns out later that the instructions in Mary's patent application don't work, that the entire patent is invalid and Mary doesn't have any rights in the invention even if there's some other way to make use of her idea.
The patent would be invalid for many reasons such as lack of sufficiency, lack of enablement and inequitable conduct. I have come across cases where the invention as disclosed cannot work as disclosed but where a small non-obvious change will make it work. That will not save the application but it opens up the possibility for claiming that patent application as your own (this is not trivial) and use it to establish a priority for subsequent applications where you do bring in sufficiency. This can happen in cases of industrial espionage.