I checked the admin panel and, unfortunately, there is no option to do that. The only way you'll know if you were quoted anywhere is to manually check for yourself.
However, there is a slightly different variation of that. If someone tags your username by putting the @ symbol in front of it, you will receive a notification in your Notifications bar at the top of each SH page (ex: it'll say "User tagged you in a topic" with a link to the post you were tagged in). It doesn't work when your username is in a quoted post, though; the username has to be written on its own in order for it to work.
This option is currently turned off, but, if people would be interested in this, I think we could turn it on.
