No. Making a photosite deeper by itself does not increase dynamic range. The useful factor is how many photons the photosite can collect and convert relative to its noise floor. If a deeper structure causes less light to reach the sensitive area, low-light performance gets worse rather than better.

In practical terms, increasing depth alone does not expand the capture range from shadows to highlights; it can just reduce the amount of light reaching the sensor, effectively shifting exposure needs without adding usable range. To improve dynamic range, a photosite generally needs greater effective light-gathering capacity, which is more closely related to its usable area and sensor design than simple depth.

So the short answer is: deeper photosites are not automatically better, and can even be worse if they block or reduce incoming light.