In short, Yes!
Residents from a state/territory that is compliant with REAL ID or non-compliant with REAL ID, but has received an extension may continue to use their current state/territory-issued driver’s licenses and identification cards, regardless of whether the card is REAL ID compliant or not, for accessing federal facilities, including military bases. This is what we call 'state-based' enforcement. Only the state that issued the resident’s license/ID must be either compliant or have been granted an extension in order for that resident to use that license/ID for accessing Federal facilities. The license/ID itself does not have to be REAL ID compliant until 'card-based' enforcement begins on May 3, 2023.
Starting February 5, 2018, residents of American Samoa, which is not compliant with REAL ID and was not granted an extension, will no longer be allowed to use their American Samoa-issued driver’s licenses and identification cards to access federal facilities (including military bases), enter nuclear power plants or board commercial aircraft. As noted above, this is what we call 'state-based' enforcement. American Samoa residents will need to show an alternative form of identification that is acceptable to the facility. Visitors should contact the facility to determine what, if any, identification is needed for access.
Where alternative forms of ID are required, typically, a government issued photo ID, such as a Passport or Passport Card, will suffice.