The adapter works on a TV screen.
Thanks for asking ahead!
Apple monitors are different from PC monitors: the most common differences are display interface (most recent Apple monitors use DisplayPort, rather than VGA, DVI, or HDMI interfaces which are more common on PCs), and Apple Cinema displays often forgo the cost of hardware scalers - they use software scaling to set lower modes on the Mac. But that doesn’t work on Windows, so you need a graphics adapter which supports the full native resolution of the display.
If you let us know what Plugable product you’re looking at, and what model of Apple monitor, we’ll be able to tell you the exact story for that combination.