Yes. Under Settings → Who can manage campaigns, tick Shop managers. They then get the Dashboard, Campaigns and Cart Timer, and can create, change and delete campaigns, their coupons included. Settings, the licence, import and export stay with administrators. Until you choose, only administrators can, and the Dashboard asks you once.
For another role, a role editor plugin can give it the trct_manage_campaigns capability. A role given that alone can run campaigns but not change which coupon one works with, which needs WooCommerce's right to edit coupons.
Still stuck? Ask the developers who wrote it. We aim to reply within one business day.
