So-called "artificial noses" can also be used to detect when food is spoiling, and in doing so, can help prevent sickness and disease. In fact, such products have already been commercialized. My guess is that medical applications carry with them the risk of error that can have substantial health and liability implications. Unless these risk factors are managed down to an acceptable level, they eill not be implemented on any kind of broad scale.

You have not defined what you mean by an "artificial nose". From the context of your question I do not expect that you are interested in smelling roses or wine.
Perhaps you have read somewhere that dogs can "smell" diseases, and are thinking that this could be used for diagnosis. If this is your line of thinking then I believe that a chromatography / MS combination could be used, and would probably be even more sensitive than a dog nose.
The first step on such a project would be to identify what compounds are responsible for odour associated with a disease. Once this is known, the rest, namely developing MS-based methodology to detect disease condition would be straightforward.

If the method is going to be used to diagnose a disease then at a minimum the methodology must be validated for at least the lab that is going to perform the test. Which method depends on what kind of molecule is of interest. For molecules you might be able to smell, as Karel says, LC/MS is likely most appropriate.

Although I agree that GC/MS is a great technology for volatiles and can be correlated to what is smelled by noses, it is costly to purchase and difficult to run with complicated data output. Certain portable GC/MS companies are making dedicated simple, cost-effective analyzers that work for specific applications like explosives detection and could be demonstrated for biomarker detection. I would suggest an alternative is to keep an eye on a company like Owlstone (owlstonenanotech.com) which has a simpler solution that has been developed for lung cancer detection using breath - simple and less expensive to own/operate.
However, like an novel technology platform in diagnostics there is a long path to validation and acceptance by the medical community. First question is whether the sensitivity and specificity are high enough to displace alternative approaches and to get credibility with health providers.

Is this sort of an AI that would work through identifying various odors? Sort of like how dogs can be trained to sniff kids' breath and tell if blood sugar is low?

You have not defined what you mean by an "artificial nose". From the context of your question I do not expect that you are interested in smelling roses or wine.
Perhaps you have read somewhere that dogs can "smell" diseases, and are thinking that this could be used for diagnosis. If this is your line of thinking then I believe that a chromatography / MS combination could be used, and would probably be even more sensitive than a dog nose.
The first step on such a project would be to identify what compounds are responsible for odour associated with a disease. Once this is known, the rest, namely developing MS-based methodology to detect disease condition would be straightforward.
Do we know

• what compounds do dogs smell when indicating a disease?
• are these compounds specific to a disease / organ / tissue?
• or are dogs alerted to some general smell because of a change in metabolism / sectetion?
• is the smell eminating from a specific body area (breath, perspiration, etc.) or
• does this also depends on the disease state?

If answers to these questions are known than GLC/LC-MS could effectively be used for diagnosing disease conditions.