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?