There is a Google search app whose tile displays as G. I wouldn't hold my breath though for Chrome for RT. They could do it easily as Metro/Modern app but have been insistent that they want access to the desktop as well (to the point of threatening litigation). Their little trained pets at Mozilla have insisted the same. Microsoft has made it clear they will not give access to the desktop APIs to anyone. It is two separate paths for Windows 8 and Start Screen only for RT.
^^ This. Make fun of Apple and their walled garden but I like how iOS apps behave properly. I want my RT apps doing the same thing. No need for Chrome to access the desktop.
I recently left a job where we were forced to use Chrome, Google Apps and a corporate Gmail account as our default desktop stuff. HATED every minute of it. Changed jobs in part because of that.