The question pretty much says it all.
For instance, if I were using, say, Twitter Bootstrap, could I define classes in my own SASS stylesheet that inherit from Boots
YES! its possible.
If you want all elements to inherit the .btn class from Twitter Bootstrap's Default buttons
.btn
In your styles.scss file you would have to first import _bootstrap.scss:
styles.scss
_bootstrap.scss
@import "_bootstrap.scss";
Then below the import:
button { @extend .btn; }