Yes. As long as you are the owner (not just an Admin) of each of the Facebook Business Pages, then you can post ads on behalf of different pages using a single PSAI account.

Ads Manager will create an ad campaign using whichever Facebook Business Page is currently connected within PSAI. To change the page you're posting from, you'll need to change your Facebook connection within your PSAI company settings, as shown below.

Please be aware that you can only have one active Facebook connection at a time. If you are posting ads for multiple Facebook pages, then you will need to change your Facebook connection each time you want to switch the account you're managing.