Does having a cadence sensor improve the accuracy of calorie calculations or other metrics?

a cadence sensor gives you accurate cadence data, nothing more :) a powermeter (which also gives you accurate cadence besides the power) can give you accuare data about the work (in kilojoules, which is ~1:1 ratio with calories if we assume 25% efficiency)

I appreciate the answer. I figured that, but wanted to confirm. I do have a cadence sensor on one of my bikes, but if it makes a difference, I would have added it to my other bike.

A power meter would be wonderful, but just way outside my budget.

For a lot of cranks you will get a budget single crank arm PM upgrade.
I*ve got a one for Rival around 200€.

So it depends on the crank, as more expensive it is as more expensive the upgrade will be.

I'm riding a vintage MTB and a folding bike (both with flat pedals), so my options are limited. LOL