You can can definitely use a UASP enabled SATA-to-USB 3.0 adapter but it will not connect with UASP and there will be no UASP speed boost as a result.
USAP is an extension to USB connection that will be enabled if it exists, but safely ignored if not. As this page on the StarTech website explains:
UASP stands for USB Attached SCSI Protocol. It allows for faster read/write data speeds to and from storage devices.
Compared to traditional USB 3.0 BOT, UASP performs up to 70% faster read speeds and 40% faster write speeds at peak performance.
As well as this; bold emphasis is mine:
Having a supported Operating System and hard drive enclosure/dock are not the only requirements for taking advantage of UASP. Your USB controller on your computer also needs to support UASP.
So if your OS and system do not support UASP, UASP will not be enabled. FWIW, most of the external enclosures and multi-connection cables (like the one you linked to) will support UASP if your system and OS support it. So it’s not really a unique feature of this UGREEN device.
That said, USB 3.0 is 5Gbps so honestly you already have decent speed for a connection like this.