Ofcourse you can create a cron job which allows you to match the products in catalog price rules table i.e. catalogrule_product using the following select statement
select distinct product_id from catalogrule_product
For the above selected products you can set 'marketing' attribute to whatever value you want to show.
The above way solves the problem you want to solve but it is not an elegant way to show your customers sale products because they need to browse through each and every category to find sale products. I would rather create a sale or offer category and show sale products in one place.
There are several extensions which allows you to do that but for our site we have used the following extensions
https://www.scommerce-mage.com/magento2-dynamic-sale-category.html
Hope it helps. Thanks