Yes, you can be both an attendee and an organization.
You can be both an attendee and an organization at the same time however, depending on which account you register as first will determine if you will be able to use the same username for both accounts.
If you register as an attendee first, then go to register as an organization, you will need to use a different username or register as an organization.
If you register as an organization first, when you go to register as an attendee you will select Register to Event on the registration page, then rather selecting Register As Attendee you will select Sign In and enter your username and password in for your organization account then follow the steps to complete your attendee account.