This is all routine, to the point of being trivial. Genome-based diagnosis is very common and is the preferred approach for many, if not most, infectious diseases. Here is a list of over 150 FDA-approved genome-based assays for pathogens.
Some quick examples include influenza:
Rapid Molecular Assays
Rapid molecular assays are a new kind of molecular influenza diagnostic test for upper respiratory tract specimens with high sensitivity and specificity.1 One platform uses isothermal nucleic acid amplification and has high sensitivity and yields results in 15 minutes or less. Another platform uses RT-PCR and has high sensitivity and produces results in approximately 20 minutes.
Other Molecular Assays
Reverse Transcription-Polymerase Chain Reaction (RT-PCR) and other molecular assays can identify the presence of influenza viral RNA in respiratory specimens with very high sensitivity and specificity.
--Influenza Signs and Symptoms and the Role of Laboratory Diagnostics
A newer test protocol (RT-PCR) is more reliable and is replacing the antigen-detecting test in many hospitals and community laboratories.
--Respiratory Syncytial Virus (RSV) Infection
Over the past several years, conventional and real-time PCR assays have been developed for detection of bacterial meningitis pathogens. Reliable assays have been extensively evaluated using invasive clinical isolates and/or clinical specimens from around the world (8, 12, 15, 17, 29, 35, 52, 60). In general, validated assays should have high sensitivity and specificity. They can be used as complementary approaches in bacterial disease diagnosis.
and many, many more.
An important trend now is using genome detection methods to look for many different potential pathogens in a single sample; these "lab on a chip" approaches (e.g. here are just entering clinics but will probably be routine in a few more years.