The old adage says that there are many paths to the truth, and I am inclined to agree. Therefore, my answer is 'no'. We do practice weapons at our dojo, although you can start as late as 5th kyu, but they are an aid, not the supremely important part of our training.
I might be very badly mistaken since I know next to nothing about the topic, but aren't here schools that don't practice weapons at all? Yoshinkan? And don't the folks in those schools do pretty good aikido now and then?