There may be some effects that way. There may also be some countervailing factors.
What I'd suggest is that, insofar as unemployment benefits cause unemployment, that can actually be a good thing.
Milton Friedman suggested once that unemployment goes down when workers lose hope for better pay. We actually want workers to have a good negotiating capability with employers. We want people to be able to spend longer to find the right workplace for them rather than less time to find a workplace that they will hate and contribute minimally to. Unemployment facilitates that.
Moreover, unemployment benefits also help people seek out appropriate education and job training. Unemployment even in relatively ideal conditions comes about when the economy makes adjustments. Climate might shift, or there may be a demographic adjustment, or there may be a technological change. When cars came into vogue, unemployment benefits would have helped carriage makers and drivers find new work. We want people to be able to spend time between jobs to be with their families, build themselves, and enter the workforce renewed.
In other words, the very point of unemployment benefits is to make unemployment a more valuable period instead of a harrowing trial. We want people to be able to quit workplaces that don't work for them or be able to risk being fired without it ending their life.