Does sending a solid arts supplement significantly improve someone’s chances?
Not ‘significantly,’ but slightly. If your grades and test scores and preparedness for Princeton level work check out, then the admissions committee will look more closely at your application, assessing for the qualitative elements. (Essays, recommendations, ECs, interviews, and yes, arts supplement). At their discretion, they will send it to the relevant department for evaluation and then use that to inform the decision. If the department said they wanted you, that would be an argument in your favor if you made it to committee. However, arts and music and dance have not nearly as much sway as sports, so don’t get your hopes up on the basis of a good supplement. It’s a very smart move to assemble one if your talents are truly top notch, but you need to have everything else as well. Any individually stellar component of your application is merely one piece of a much, much larger puzzle. Put your best foot forward, and past that it’s a random crapshoot.
Good luck to you.
I felt like sending an art supplement worked positively for me. I had done art in high school for four years, so I had a pretty comprehensive portfolio, with about 15-20 strong pieces in various media. If you have a strong portfolio and feel that art is something you’d like to emphasise in your application (for example, my essays were also art-themed), I’d suggest sending it. It shows the admissions officers an extra side to your personality - in addition to learning about who you are, they can see how you express yourself and what you can make.