That's hard to answer. Die hard Trump supporters will say, "Yes, he does!" But we don't really know.
However, he could have leverage against the federal bureaucracy by threatening to do it. Michael Bargo, Jr., tells us in How Trump Can Defeat the Establishment Bureaucracy that federal employee unions were created by President Kennedy in 1962 with an executive order. And President Trump could revoke it if he wanted to.
Here are some interesting numbers pulled from Mr. Bargo's article:
The SEIU is headquartered in Washington and has 1.9 million members. Since 1989 the SEIU has given $238 million to political candidates, making them the number one political contributor with 100% going to Democrats. The number three biggest contributor is the National Education Association, their 3 million members having given $114 million, 97% going to Democrats. The number four contributor is the American Federation of State, County and Municipal Employees. Their 1.6 million members gave $100 million with 99% going to Democrats. The number nine biggest contributor is the American Federation of Teachers who gave $81 million, 100% going to Democrats. They have 1.6 million members in 3,000 localities nationwide.
These four unions, active throughout the U.S., have a total of 8.1 million active members and since 1989 have given $533 million to political candidates, 98% of which went to Democrats. And this number does not include the other municipal public sector unions, etc. which amount to about 12 million members, giving a total number of public union members of 20.2 million. This is the size of the bureaucratic opposition Trump has in the states and Federal government. On the Federal level, there are 45,000 Federal employees in Chicago alone. About 28% of all Federal workers are union members.
I suppose the silver lining is that only 28% of federal workers belong to a union. But even then we can be sure that Democrats in Congress will fight tooth and nail to keep the unions as loyal contributors to their own coffers.