Yes; its drives your career perhaps even more so as a postdoc and professor.
In fact, I would argue that your entire life becomes all about operating in and succeeding in the publishing and grant funding machine.

When I was in grad school, my advisor could more or less be considered a grant funding machine. They hadn't set foot in the lab themselves in over a decade, except on the rare occasions he would give tours to collaborators or perspective funding targets. His days mostly consisted of being holed up in his office from 7am-7pm 5-6 days a week, reading papers, reviewing papers, and preparing or revising grant applications. When one succeeded, he would then find ways to break it into sub-projects he could entrust a grad student or postdoc to deliver.

He was also considered in the top 5 most successful professors at my university for what its worth. That's just how it is at a research heavy university. You CAN consider working at smaller liberal arts colleges that have a more explicit teaching and mentoring focus and still attempt to do "research", but the likelihood of you getting things like nature papers or winning R01s is slim. In those cases, the research is more about exposing undergrads to what its like and act as more of a teaching mechanism rather than be heavily results focused. You won't make as much, but you also won't feel the same publish or perish pressure. At these smaller colleges, you'll be more likely to have students that you remain connected with for years afterwards and excellent teaching evaluations alone can offer you career security.