Well, indirectly it could be possible. You'd need some device that connects to the drive's SATA power plug in question. Similar to the existing power monitoring hardware for GPUs that connect to the PCIe power plugs, like the TG WireView. Such device would measure the data and provide that data via a USB interface. But then it would also need some software that reads the data, processes it and displays the result to the user.
Not sure if there is something like this out there, but I doubt it because the power consumption of such devices is so low (with the exception of >= 10k RPM drives) that it's not that relevant. And if you want to measure the power consumption of multiple SATA devices at the same time, you'd need multiple such measuring devices.