I think you’re referring to the boycotting of buying products (correct me if i’m wrong). If we are thinking in a strictly demand-supply framework for goods (which I think you are), then there are two things that could happen. First is that a boycott of impactful size would shift the demand curve for goods inward. All else equal, this would lead to a reduction in the quantity demanded and supplied of the good, and the price of the good would fall (see figure 1). In a lot of intro level economic theory, this is where we stop due since we tend to invoke the concept of ceteris paribus. Though what you’re saying is that a reduction in demand for goods may have adverse affects on the labor market. Figure 2 describes the effect of a shift in preferences for a given labor market. For example, consider we are looking at the market for Nestle products (as shown in Figure 1). In Figure 2, we are examining the labor demands for the Nestle company. Given a negative shock to the demand for Nestle products, the demand curve for workers at Nestle will shift to the left.

What happens next relies on what theory of wages you subscribe to. If you subscribe to the theory that wages are sticky (most are since you never hear of less pay being offered, but instead less jobs being offered), then you will see substantial unemployment occur (Figure 2). If you subscribe to the theory that wages are flexible, then wages will lower to account for the loss of income from the company due to reduced demand, but employment would stay the same, just at a lower wage level (Figure 3). There is much more evidence for sticky wages, so in general, I would agree with your statement. (Source: I am a Ph.D. candidate in Economics and am teaching labor economics for undergraduates).

All this being said, using demand-supply to illustrate real-world outcomes will always fall short. Intro level economics provides useful tools and models to help conceptualize the world, but the world does not operate under the strict conditions that make these models possible.