I would not expect that. Public employees whether in a union or not, have disproportionate influence more because they put boots on the ground, rather than shell out campaign money.
My county of Columbia, NY is run by a Pub machine. About 90% of the county employees are registered Pubs, and that is no accident. They are expected to work in campaigns, do party grassroots work, show up and contribute to Pub candidate fund raisers, and if they don't toe the line, their employment situation becomes more difficult and unpleasant. Heck I was trying to get this Independence voter to sign a candidate petition, and he said well I like the candidate, but she is a Dem, so I can't do that, and what I really need to do is reregister as a Pub. He was a county employee. One of my little goals in my life is to destroy that machine before I die. It is extremely offensive and disgusting.