Yes, you can use one user account to access Boardable accounts for multiple boards. To do so, you must use the same login email for all Boardable accounts.

In order to toggle between the various accounts, go to the left-hand side beneath the org logo (if one is uploaded), select "switch accounts," and a drop-down list of the all board accounts associated with that login email will appear. This is also where one goes if wishing to create another Boardable account for a separate organization.