By default, no. But you have several ways to indicate it somehow:
Using the name of the product in the title or the description of the campaign.
Creating different campaign folders in the navigation tree (if you use Campaign v6/v7) or programs (if you use Campaign Standard) that you name according to a product, then you would add your campaigns in the relevant ones.
Extend the campaign table to create a link with your custom product table. Then you'd be able to specify a product for a campaign. This can be done similarly to what was done for creating your product table (as I guess you created one since it's not available OOB).
Let me know if there is a solution here that you prefer and if you need further help while exploring considering your options. Last solution is a bit more complex if you do not know how to manipulate schemas.