I don't think it does. Though my udev rules don't work on it, since only the adapter controller is exposed to udev. But smartctl works fine. smartctl-detect script as a workaround, if the controller shows up.
About power, the HDD either gets enough or it doesn't spin at all, makes clicking noises. I have the same adapter and it's only good for SATA-SSDs (they draw less), normal slim 2,5" HDD need additional power.
In short, no, get an adapter with two cables or power plug. Or maybe, if something like this exists, one with USB-C, that should pull enough (but read the specs).
Btw, mine has now >100 "time in under-temperature" warnings, because it isn't in warm case on spin-up i guess. But it doesn't do any damage in this case.