Hi mj1984,
The canonical tag is your only option here. The problem with duplicate content is really about control:
(i) Controlling Link Juice (past + future)
(ii) Controlling the targeted landing page within your campaign
Google will devalue certain identical pages, but they will always favour one. They do not, as far as I am aware, devalue all content that is duplicated (including the original) - So your concern isn't that your site is being devalued, simpliciter (often an immediate unwarranted concern). It is that Google will select one duplicate page and favour that above the others.
The canonical tag exists for you to control this.
So, will Google recognise there is no duplicate content?. It should, it might not, but I wouldn't worry about this. For the canonical tags that it does pick up (& eventually) - you can be confident that the page you want to rank, will be the one ranking.