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Building on the point by JBT, the saxophone is a truncated cone. After the mouthpiece, the cone "ends" in your oral cavity. Just a longer way of me saying that if the mouthpiece is approximately conical, it would work.

Additionally, as JBT mentions, it's difficult to make a true cone with PVC. You could try for a wrapped straight-ish design, like the Eppelsheim Tubax (which is why that some people argue that the Tubaxes aren't true saxophones) or, instead of a sax, go for a contrabass clarinet design. People HAVE made those with fairly good success.

It's interesting that the carrot-based horn was mentioned. A carrot is roughly conical ....
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