Hi Nick,
From your description, I understand that you want to upgrade your current active directory, enable DirSync and migrate the Exchange 2003 server to Office 365 Exchange Online.
Actually, we recommend you first upgrade the 2003 Active directory server to 2012. Given the subsequent operation that you would like to migrate user mailbox to Exchange online, for cutover migration or staged migration, upgrading the AD will benefit to the process of the migration, for example, we need to install and configure a directory synchronization tool before we can run a staged Exchange migration.
Here is the reference:
Migrate Mailboxes to the Cloud with a Staged Exchange Migration
help.outlook.com/.../ff959224.aspx
Please feel free to post back for more help.
Thanks,
April Zhou