This is now possible with custom properties:

.brown { --rgb: 118, 76, 41; }
.green { --rgb: 51, 91, 11; }

a { display: block; position: relative; }
div { position: absolute; bottom: 0; background-color: rgba(var(--rgb), 0.8); }
a:hover div { background-color: rgba(var(--rgb), 1); }

To understand how this works, see How do I apply opacity to a CSS color variable?

If custom properties are not an option, see the original answer below.


Unfortunately, no, you'll have to specify the red, green and blue values again for each individual class:

a { display: block; position: relative; }

.brown { position: absolute; bottom: 0; background-color: rgba(118, 76, 41, 0.8); }
a:hover .brown { background-color: rgba(118, 76, 41, 1); }

.green { position: absolute; bottom: 0; background-color: rgba(51, 91, 11, 0.8); }
a:hover .green { background-color: rgba(51, 91, 11, 1); }

You can only use the inherit keyword alone as a value for the property, and even then the use of inherit isn't appropriate here.