I haven't witnessed what happens if the members were determined to anyway, or read up on the circumstances of past wildcat strikes.
Also, the last time I saw something about my local hospital nurses' union in the news, they were alleging that the recruiting and employment of foreign nurses violated human trafficking laws. Basically, they signed people up from another country with a huge penalty if they quit early as "compensation" for the cost of importation.
To me, that strongly suggested the union was not playing a strong hand, when it comes to "unsafe policies".