As far as I know, the current QA Checker > Iconsistencies function does *not* check against the registered TMs for the project.
It would be great to have this feature especially for server-based TMs.
While this feature is possible with the API, connecting to server-based TMs is a hassle as you need to have the user credentials to access the TMs.
Currently there is no way to automatically retrieve the credentials using the API, and the developer is required to ask the user to input there credentials for *every* project.