Not a chance.
To the contrary, NSA is a component of the DoD acting under the authority of the Director of National Intelligence (DNI). The other services act as collectors, in part, for NSA.
NSA is the agency with the mandate from Congress when it comes to electronic intelligence and counter-intelligence.
The services rely on NSA as much as NSA relies on them.
WWG1WGA
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)