I don't know of any way to put the entire row into edit mode with the DataGrid that comes with Silverlight.
When you have a cell that is NOT marked readonly, you can double click the cell to enter edit mode, then press tab to get to the next cell and it too will be in edit mode. You can then continue pressing tab to go to the next row and the cells will remain in edit mode. Pressing F2 when your focus is in a cell will put the cell into edit mode. The cursor keys allow you to navigate cells and rows. This is pretty close to what you are asking.
Perhaps one of the 3rd party grids may support this functionality.
EDIT
Here is another discussion on How can I put a Silverlight 3 DataGridCell into edit mode in code? maybe it's conclusion will be of some help or the answer to How do I Immediately Validate a Newly Inserted Row in a Silverlight 3 Datagrid? might work for you.