Yes, you can query the URL:
http://suggestqueries.google.com/complete/search?client=firefox&q=YOURQUERY
For example, http://suggestqueries.google.com/complete/search?client=firefox&q=justin
will return:
["justin",["justin bieber","justin timberlake","justin tv","justin timberlake tour","justin boots","justin blackmon","justin baldoni","justin bieber twitter","justin long","justin moore"]]