I've moved my email accounts to Google Apps a few weeks ago and I'm quite glad with it. The search is great and I looked for a way to search my Inbox directly from the Firefox search box without another addon. After looking around I've found a way through the Opensearch capability of firefox. Since it's handy I wanted to share it with you even when it's not strictly design related ;-). Just make a text document with the the extension .xml in the Program Files/Mozilla Firefox/searchplugins directory (on Windows) /Applications/Firefox.app/Contents/MacOS?/Search/Plugins/ for Mac, cut and paste the following lines of code and replace the highlighted parts (Shortname, Description, yourdomain.com) with your details.
<?xml version="1.0" encoding="UTF-8"?>
<OpenSearchDescription xmlns="http://a9.com/-/spec/opensearch/1.1/">
<ShortName>My Gmail</ShortName>
<Description>My Emails on Google Appz</Description>
<Url type="text/html" template="https://mail.google.com/a/yourdomain.com/#search/{searchTerms}"/>
</OpenSearchDescription>
After saving the file (eg. mygmail.xml) restart Firefox and you will see the new search engine in the drop down box.
Note: This works only with Gmail for Google Apps and if you choosen to remain logged in - to find out more about Google Appz follow this link.