Yes and no.
I also feel I should say: I'm still using a Sanwa JLF lever in my arcade stick and I'm by no means an expert. That all said, I totally see it as a matter of what you're most comfortable with. To me, the stick is for the experience just as much as precision. The feel of the buttons, the clicky lever, the heft and weight. I often find my venerable Saturn pad more 1:1 with my intentions if anything, but some swear by sticks. Even more, I find the prospect of playing Shmups on a keyboard horrifying, but to many it's the only way. I think you can get great results with whatever input method you practice. Maybe I'll change my tune when I eventually get a Seimitsu lever.
In my opinion you should totally get a stick, but mainly because it's a lot of fun!
It was a long wait between knowing of Batsugun Special and actually playing it, and it really exceeded my expectations! I was expecting to simply appreciate the game symbolically for being the first danmaku, but WOW is this game good! The levels are all so well designed and lively, and all three ship types rule! I haven't cleared a full loop yet, but I'm hyped to see what else is in store.
Touhou rules. I got into it because of Japanese Donald McDonald, but it's taught me so much about how to Bullet Hell. AND IT HAS CIRNO!