Short Answer: No
Good question. The feature you are talking about is known as inheritance. Essentially, will a child element inherit a parent's font-family if its own specified font-family is not installed on the user's computer.
I couldn't find any explicit documentation although this specification could be taken to mean that no inheritance will occur in this case. Therefore, to make sure, I tested out the latest stable build of Firefox with the following:
<body>
<p>Hello</p>
</body>
body {font-family: Arial;}
p {font-family: Quill;}
I don't have Quill installed but I do have Arial. However, despite this fact, the p element is rendered in the default serif font, not in Arial.
Since there is at least one major browser that functions in this way, in order to ensure consistency, you should always use this instead:
body {font-family: Arial;}
p {font-family: Quill, Arial;}
Thinking more about this, one way to fix this would be to allow the following:
p {font-family: Quill, inherit}
p {font-family: Quill, default}
The second rule is essentially what browsers do at the moment, but only implicitly. If CSS allowed us to specify the last property explicitly, we could alter this behaviour. Unfortunately, this does not work currently. Anybody know how to submit suggestions to the w3C?