Google Drive app on Nexus 7 doesn't allow offline editing
From the looks of it, at this point, marking something available offline only allows you to read it offline when using a mobile device (Source). However, you can edit and write files offline if you are using a computer or device running Chrome or Chrome OS. I'm sure at some point Google will allow editing offline, especially for tablets, but at this point, I am pretty sure that you can online view files offline. Sorry.