Yes,
www.mozilla.org is doing it, for example:
----------------------------------
http://www.mozilla.org/GET / HTTP/1.1
Host: www.mozilla.org
User-Agent: Mozilla/5.0 (X11; U; Linux i686; es-ES; rv:1.8.1) Gecko/20061010 Firefox/2.0
Accept: text/xml,application/xml,application/xhtml+xml,text/html;q=0.9,text/plain;q=0.8,image/png,*/*;q=0.5
Accept-Language: es-es,es;q=0.8,en-us;q=0.5,en;q=0.3
Accept-Encoding: gzip,deflate
Accept-Charset: ISO-8859-1,utf-8;q=0.7,*;q=0.7
Keep-Alive: 300
Connection: keep-alive
HTTP/1.x 200 OK
Age: 449
Date: Mon, 29 Oct 2007 19:25:01 GMT
Expires: Mon, 29 Oct 2007 19:35:01 GMT
Cache-Control: max-age=600
Connection: Keep-Alive
Via: NS-CACHE-6.1: 1
Etag: "2b5a-cc8b36c0"
Server: Apache/2.0.52 (Red Hat)
Last-Modified: Thu, 25 Oct 2007 20:08:35 GMT
Accept-Ranges: bytes
Content-Type: text/html
Content-Encoding: gzip
Content-Length: 3068
----------------------------------
That's the data from the headers given by the firefox plugin.
