For a lecturer (defined generically) it would be very important anywhere. Most of your competition for any teaching position will include many people with experience. Some will have a lot. It is good to get it wherever you can.
I have no experience with the program you point to, but it looks promising. But there are other ways. I'm surprised that you aren't getting some of that in your doctoral program, but that depends on funding. One way to easily get a bit of experience that may be open to you is to ask a professor who also has undergraduate teaching duties if you could give a lecture or two on some topic in that other course.
When I was an undergraduate, my professor actually asked each of the students (very small classes) to deliver a lecture on some topic. It didn't give him the day off, however, as he was there and gave us some feedback on how we did. The first try can be pretty miserable, actually. Especially for an introvert.
You can develop a teaching philosophy of sorts by watching the professors you admire and giving some thought to why you think they are effective. What is it that they do, not just in the lecture hall, but overall, that makes you appreciate them. You can even ask them about it.
But many new PhDs have a lot of misconceptions about teaching and learning. The biggest misconception, I think, is to believe that students are all like yourself. They aren't. And you need to adapt to that if you want to be effective. Effective lecturing, for example, is only a very small part of teaching.
However, since the term lecturer (descriptive, generic) may be different from Lecturer (an entry level academic rank in UK) your mileage may vary. How important it is for hiring into a specific rank depends on the university hiring. For some, teaching would be very important. For others only research really counts. For some even research isn't enough unless you attract grant funding for it.