I applied once.. years ago, didn't hear back, and I knew that dream died quickly. But I've worked a few jobs since then, and after applying to hundreds of jobs recently, hoping one would land and forgetting that I'd even applied, a rep called me to remind me that I had an orientation to attend with Google.
I had a few other interviews for coding positions and other non-tech industry positions and I could wait it out, but Google hired me immediately after I took a test and passed. And now I figure having Google on my resume, whether my time here lasts a month, three months, six months, or a year... it's a blessing to me no matter what.
Just looking out for the future, do companies actually notice or care if Google is on your resume?
Even if you only interned at google, people will notice.