Can you use DeepSpeech with a Translation Software tool, such as SDL Trados?
The obvious answer is yes, pretty much any software can be used with any other software, it’s just a matter of writing more software.
The more useful answer will require more details about what your setup is and what you want to do. 
Also, feel free to join us on the Mozilla Matrix to discuss in realtime.
I responded to you on Matrix. There may be a delay as we are in different timezones.