Question: Does having an alien number make an individual authorized to work in the US? Or perhaps better stated-what is the significance of an alien number?

Answer: An “alien number” (or “A-Number”) in and of itself does not provide work authorization to a foreign national. An alien number is simply the reference number for an “alien file” or “A-File,” which is the record that contains copies of information regarding all transactions involving an individual as he or she passes through the U.S. immigration and inspection process.

Just a number...
Alien numbers reference "A-Files" - the immigration record for foreign nationals. A-File records are retained for 75 years!

An A-File may include information such as applications and petitions submitted; vital documents (e.g., birth certificates, passports, marriage certificates); biometric information (e.g., photographs, fingerprints); enforcement supporting documents (e.g., RAP sheets); and other documents such as tax returns, correspondence, and interview notes. The information in an A-File is used by USCIS and other DHS agencies for immigration benefits processing, law enforcement, and national security purposes.

An A-File and the corresponding A-Number may be generated as result of filing an application for employment authorization. For example, a student may receive an alien number as the result of filing an application for an Employment Authorization Document. An A-File and A-Number may also be generated as result of an enforcement action, e.g., when a foreign national is denied admission to the U.S. and a record of the denial is created and sworn statement taken. A-File records are retained for 75 years from the date the file is “retired” to the National Archives and Records Administration or from the last date of action and then destroyed.