No. Just no. The back button goes back. Period.
The close button closes modal windows overlaying the original page and originating from the same site.
I can already hear you countering "But.. since the content is served from google.com due to caching, this pattern is technically correct".
Which is tantamount to saying "We serve the content. So we can add whatever the heck we want"
Very frigging clever Google. Well done. /s