Earlier quoted context omitted.
I've definitely caught inappropriate communications behind my back, to the point that I've had to pursue litigation and have collected a couple of (small) tortious interference settlements. This is much much bigger issue to any employer than any union-forming issue. An employee who sues is a giant nightmare. (Which I will say right now can be unfair, because it's hard for an outsider to distinguish between the bogus…
An employee willing to sue when the employer steps out of line, seems like exactly the sort of thing that should be protected. Employers should not be allowed to do wrong things. Employers should especially not be allowed to penalize, nor work together to be aware of or penalize, employees that "tend to sue".
However, even without deliberately asking, a company could learn, and it's not hard to imagine why an employer would be very wary of hiring someone who has sued a former employer. Being sued is an extremely stressful thing and lots of people go to great, even possibly irrational, lengths to avoid it.
Ask how you would feel working for a company that had sued former employees.
There are no good answers.