Over the years I have known a bunch of people who work at the EPA, either as lawyers or in some other career civil service position. There might be some exceptions somewhere, but in my experience the only reason anyone goes to work for the EPA is because they are concerned about the environment and want to do something to make it better. Trump can executive order anything he wants but that won't change the character of the people in the Department.
Okay, the new policy could make some of the committed people quit, but not all of them. And whoever doesn't quit is not going to stop being a true believer because there is an environment-destroying neanderthal at the helm. If they feel that their agency is purposely suppressing information, they will find a way to get that information out, especially if the suppressed information directly relates to the concerns that got them to work for the EPA in the first place. In fact, by creating an atmosphere of information suppression, the President has probably made it even more likely that people in the agency will leak information to the media.
Take it from a labor lawyer, heavy-handed workplace policies often backfire. If Trump really wanted less information to get out of the agency he should have let them continue to tweet but created a really cumbersome and annoying social media policy governing those tweets. So long as people aren't told they are muzzled, they will put up with all kinds of bureaucratic shit. They are experienced federal workers after all.