Thanks for that detail. Unfortunately the ASUS website for that drive does not provide any detail on power requirements. So we have to assume that any "standard" SATA power supply connection from a PSU would be sufficient. The SATA standards do not specify any general power supply values. They do require that the connectors and cable be able to carry three different supply Voltages at up to 4.5 A each, but that does NOT tell us what any particular SATA device may use. Of the three Voltages, very few SATA devices actually use the 3.3 VDC supply, and I doubt that optical drive would need that. I expect the max current from the 5 VDC supply required by that optical drive (doubtless for its electronics) is available easily from the power supplied by the USB3 port you plug that adapter into. And I am sure the 12 VDC power supply module supplied with the adapter (which you MUST use), capable of up to 2.0 A, is sufficient for the motors of the drive. So in summary it certainly appears that the adapter you linked CAN supply all the power the drive needs. Of course, it also provides the data communication needs, too.
I would point to one small caution. The adapter says it is usable also with a USB2 port. That is true in many ways except one. A USB2 port can supply 5VDC power up to 0.5 A, whereas a USB3 port can do better at up to 0.9 A. Of course, USB3 is also much faster at data transfer rate. But consider that we do NOT know what current max that optical drive needs at 5 VDC. IF it is over 0.5 A but less than 0.9 A, then this system can work only using a USB3 port. Further, because of this power requirement, I strongly advise you use this system connected directly to a computer USB3 port and NOT via a simple unpowered USB3 Hub. If you ARE going to use it though a USB3 Hub, make sure that Hub has its own power supply module to ensure all output ports do provide the full standard power.