By chaining two systems you are making the performance of BlueConic dependent on the performance of your tag management system.
The engineers of BlueConic are constantly working to maximize the performance of BlueConic, in order to let BlueConic adapt your page in real-time without visitors noticing. The use of a tag management system however will delay BlueConic's response, because the tag first need to be placed, before BlueConic can take action. This will always lead to a little extra delay in BlueConic's actions, depending on the setup and performance of your tag management solution. This may result in noticeable flickering of content.
Note: Tag management systems are designed to manage all kinds of tags, such as advertising or affiliate trackers that change and vary often over time for different pages. The BlueConic script however is static and will have a long-term relation on a page, in which case a Tag management system will not have extra benefits except during the initial setup.