Opera works perfectly (and has) with adwords/adsense/blogger/wmt
Only rarely has Google code not worked in opera. Most often you can over come it by masking your user agent. All you have to do is change your user agent.
-> visit google (or the problem site)
-> click F12
-> edit site preferences
-> click network
-> click 'browser identification'
-> switch to "mask as firefox" in the drop down.