If dragging was occurring in smooth water only due to wind speed, I might think something like that would be fairly easy to develop and use. You'd have a nice, steady, frequency that suddenly dropped pitch when the anchor let go, However, boat motion is typically wild during a dragging event. If you convert the tension to sound, the anchor rode is going from slack to a pitch that only dogs can hear. And the seas are not a clean sine wave typically. If we assumed dragging was a steady condition, rather than a jerking snatching rodeo, draggng in muck, sand, or on rock would seem to produce different signatures. A fouled anchor would likely produce different signatures as well.
The exception might be similar to my dragging event in the river, where the anchor briefly grabbed on the muck and vegetation, then the vegetation broke loose, turning the anchor into a dragging muck ball. Happened quickly, and in protected water, so I had very close land references to tell I was dragging. Rode tension went up, then fell back as dragging commenced.
Back to the case we'd be interested in. Dark, no land references, possible storm conditions. There should be an audible difference in the "rode music", when dragging, if you convert the rode tension to an audible signal. Unless you could develop software that could recognize the change and only produce a light or buzz when dragging, it might just add to the stress of whatever is going on. Hearing the rode tension converted to an audible signal, essentially listening to the rode stress, added to the storm sounds that are causing the rode stress, might be a bit unnerving. Maybe you could convert it to play actual tunes. Upon the solid rock I stand (holding); or Come Sail Away (dragging).
Now, if you can figure out how to separate the rode tension from anchor dragging, that would be exceptional. After all, anything that touched the string can be heard in the tin cans...
But, hey, we won't know until you test the prototype!

It is a very interesting concept. I'm not aware of any device currently performing in this manner. Good luck.