We have a 16 Exchange 2013 Mailbox Databases. Of those 16, 12 have been 'Excluded from Provisioning'. 
We are trying to come up with a script or at least command to enable-mailbox for existing AD user accounts. 

The question is, we want the enable-mailbox command to balance or randomly create mailboxes across databases and not just on one specific database. 

Can this be done? 

Divide the database to spell:
DB(AB)
DB(CD) ...
and make the powershell script, which is the first letter in the e-mail will assign the appropriate database.

Hi,

From your description, I would like to clarify the following thing:

Automatic distribution is used when you don't specify the Database parameter on the Enable-Mailbox cmdlet. This process randomly distributes mailboxes across all of the suitable mailbox databases in your organization.

If you also want the mailboxes to be distributed to the other 12 databases, you can run the cmdlet below to set the IsExcludedFromProvisioning to $false for them.

Set-MailboxDatabase <database name> -IsExcludedFromProvisioning $false

Hope my clarification can be helpful to you.

Best regards,

Awesome, thank you both.