No one knows for certain so we can only go on telltale signs. This product seems closer to a SSD with USB interface than the classic USB pendrive. It's basically a SSD featuring a USB pendrive formfactor.
For starters it supports TRIM which is indicative of the controller performing background tasks such as garbage collection when idle:

Again, this device is an actual SSD drive, not a classic USB Flash Drive or Pendrive and as such it is likely it will do more advanced tasks like refreshing data.
This idea is also supported if we take a closer look at the controller, the SM2320 which has all the characteristics of a modern SSD controller that works with modern NAND, see https://www.siliconmotion.com/download/3fu/a/SM2320_PB_EN.pdf. Modern NAND relies for integrity on such background tasks such as data refreshing.
The 'Interface' is irrelevant when it comes to answering the question if the drive does background maintenance. If it does, it needs nothing from the host except being powered on. I mention TRIM purely to establish we're dealing with a 'real' SSD rather than some beefed up USB flash drive / pendrive / USB stick etc..
So very likely this particular drive will benefit from having it powered on so it can perform background maintenance.