No. There's basically a chicken and egg problem. It is not illegal to discuss unions in the workplace or to pledge support for a union. But the "union" has no standing to do anything other than talk to people.

So to get a union you first need people to talk to their colleagues, and if the people they're talking to seem agreeable, get them to sign a card saying that they would like to be in a union. Once they have enough of these cards that have been signed by people who have spoken with union representatives and pledged their support for a union, they can go to the company and use the cards as proof that the union has broad support.

The idea that people are compelled to sign union cards is a bit of a fiction. Signing a union card is an act of bravery because it paints a target on your back especially if the union drive fails. It's documentary evidence that you're a troublemaker.