I have Visual Studio Online (now VS Team Services) account as a part of my MSDN subscription. I managed to create a project there, set a workspace in my local Visual Studio 2013
The other answers are old but I found this through Google so I think an update is needed.
Yes, you can edit a text file in Visual Studio Team Services (formerly Visual Studio Online).
Go to Code->Files. Select the file. Click Edit. Edit the file. Click Save.
If that file is being monitored by a build definition then a build will be kicked off.
This editing is not limited to Azure Website projects. What those other posters are referring to is you can edit code that is already deployed to a website. This is different becasue it is editing code in the repo.