You can almost confidently say that different level of extraction yields will taste different but can you say the inverse is true (same extraction yield = same taste)?
In my opinion, the refractometry measurement can give you an inkling where the process sits on the extraction yield spectrum. But I argue that there is no substitute for tasting. As subjective as our palate may be, you will still need to taste the shot to evaluate the taste. For example, for what it's worth, my Helor 101 hand grinder can achieve similar extraction level with my big conicals, but they clearly don't taste the same to me.
So I am trying to rationalize why I don't see a statistically significant difference in TDS/EY yet the tasting suggests there may be subtle differences. I think there are three main reasons:
The nature of refractometry measurement: Refractometer works by passing light through a liquid phase and depending on how much the light is scatteredrefracted/bent, it predicts the amount of dissolved solids based on what it was calibrated on. There lies the shortcoming of refractometry measurements - assuming the refractometer was calibrated properly (using the right technique and right calibration solution), it can only tell you roughly how much bulk dissolved solids you have, but it has zero information on the chemical/flavor molecules composition. It's akin to telling you how many apples you have in the promotion bag you just purchased in the supermarket clearance last night, but doesn't let you know how many of them were bad apples.

Limit of detection : Human palate have a taste sensitivity of around 5-400 ppm (that's 0.005- 0.4 mg/ml or 0.0005-0.04% TDS)*. The accuracy of of VST TDS meter starts at ± 0.05% TDS (or 0.5 mg/ml). That is just the instrument error alone and it is already higher than the taste sensitivity. To draw on another analogy, this time related to coffee, this is like trying to measure the coffee particle size using a regular ruler.

*https://onlinelibrary.wiley.com/doi/pdf ... .tb03598.x
Human factor: One major factor, without a doubt, is the huge variation due to human factor.

With all these factors combined, even if I (the operator) am a perfect scientist with absolute precision, my limit of detection is still above the tasting threshold. I will also have the issue of not knowing what exactly have I detected/measured in my sample. In practice, >0.3 TDS % (or more) variation is normal for me even when I do everything in the same way (same coffee, similar extraction time/ratio etc). So all hope is lost if you want to put a taste label to the resulted extraction yield %!
So in my opinion, TLDR (or if it got too technical): Refractometer measurement is not sensitive enough to account for subtle taste difference, and the measurement doesn't account for the chemical composition. Most of us are not trained enough (if it is at all possible to achieve zero variation) to do the measurement with enough precision.
This is not to say refractometer is useless (far from it, they can definitely be useful in some scenarios), but I think it should not be the only guideline to evaluate anything, especially not without a proper context.
That's just my way of rationalizing what I am seeing and by no means tested or proven, so take it with a big grain of salt! But I am keen to hear what you think about it. Have you done EY measurements across different grinders/machines using the same coffee and notice the same observation?