It wouldn’t matter whether or not union wages were tied to the minimum wage. Minimum wages raise union wages regardless of legal conditions. Minimum wages raises union wages by criminalizing the hiring of low-wage workers. With a minimum wage, businesses can no longer configure production with more low-wage labor, but must find a configuration with more high-wage labor and more productive capital. Walter Williams tells the story about how, when he was a youngster, businesses would hire a gang of teenagers to move boxes in a warehouse, but with the minimum wage it was cheaper to hire one union workers and a forklift to do the same job.
Take a look at Williams’s book, The State against Blacks.