As you say, even "if basic bioscience research stopped [in its entirety], it would be years before the effects trickled out publicly." If the consequences of a strike are not grave to the employer (even if you could get everyone on board), then the power backing the union is greatly diminished.
Yet somehow the power backing their union has historically not been "greatly diminished," at least not compared to other unions.
* A movie/show being delayed mostly has extreme financial consequences for the studio employer, not for the individual writer employees. By contrast, a scientific publication being delayed mostly has extreme career consequences for the individual scientist employees, not for their employer institution.
* The NIH's funding comes from the US government. A studio's revenue comes from the audience. NIH funding is unlikely to decrease as the result of a researcher strike, whereas a studio's revenue will unequivocally decrease as the result of a writer strike.
* Few people outside of the scientific community will directly perceive the consequences of NIH research being postponed for a few months. On the other hand, many people who enjoy watching movies/TV will directly feel the impact of favorite shows being postponed or cancelled.
* As demonstrated in [0], the effects of the strike are already glaringly evident after just a month, and will be even more evident after a few more months.
[0] https://en.wikipedia.org/wiki/List_of_productions_impacted_b...
The pressure instead is social and political. Union-friendly politicians would haul the NIH administrators in to grill them about why they're blocking cures and cheating scientists.
Thus, if some of the scientists in the union continue to work surreptitiously, it would have little impact on the effectiveness of the strike.