It's very uncertain whether the UAW's appeal will be successful. Lydia DePillis points to competing precedents. On the one hand:
... the Board has seen the reverse situation, in which politicians endorsed a union. In 2011, for example, the Communications Workers of America won an election at Affiliated Computer Services, which New York State had retained to set up its EZPass system for road tolls. The company objected, saying that a U.S. congressman and a New York State senator had influenced the election by making statements in favor of the union -- and also by pointing out that they sat on committees that oversaw the company's business.On the other hand:
The Board disagreed, ruling that “public officials, even public officials involved in the regulation of the employer’s industry, like other third parties, are not required to remain neutral and may properly seek to persuade employees.”
... in 2000, the Board ruled that politicians in the Northern Mariana Islands had sullied an election by targeting non-residents who voted to join a hotel union. The D.C. Circuit reversed its decision for lack of evidence, but didn't touch the principle that lawmakers had the power to create an untenable environment of fear.Getting a new vote is a long shot, and winning it is an even longer one, given the dedication to intimidation shown by Republicans and outside groups, as well as the fact that some significant chunk of the plant's workers would be unlikely ever to vote for a union, given the anti-union environment of the south. The threats from Corker and other Tennessee Republicans were all upside down—they weren't going to face any personal penalties, and they had the opportunity to make a difference in a close election.