No, absolutely not !Yea i know a dwc grower that uses teas to get rid of root rot.
But to awnser your question, mychos does not help kill root rot. It acts as a infection in which helps the roots to be able to better intake npks, particularly phos.
Keep doing what your doing, but dont add mychos, its a waste of money and mychos.
You can however do a side by side and see for your self, one plant with mychos in the tea, the other with no mycho in the teas.
Mychos does kill the root rot and all so eats away all the infected and dead roots ( living in the Rhizophere) until the root system is Clean and pure white, then they run out of food and die and eat each other until they are all gone ( no soil to sustain life ). There for you must replenish in DWC. There is nothing but all ready broken down synthetic nutrients in a DWC system , Mychos are not breaking down NPK in a system to feed the plant.
If I was to run one with and one with out , one wood have root slime and the other wouldn't. That is all.
There a several ways to keep a system clean
1 Bennies/Mychos ( I prefer ) teas , Great white , Pondzyme etc
2 Bleach
3 water tempature