Adobe does not recommend or support deploying DTM libraries asynchronously. When implemented in this manner, much of the functionality of DTM is lost.
For example:
Firing rules at the top of the page wouldn't work consistently. Asynchronous embed code causes the library file to load and parse by the browser at any point instead of where it is set to fire.
Best practice is to implement DTM synchronously, and then deploy scripts and tags via the DTM interface asynchronously as desired. If it is not an option, the code can be implemented asynchronously using one of the asynchronous JavaScript methods. However, keep in mind implementing in this manner can affect rule functionality.