No. To an external application, a DGV is just a collection of Windows - it doesn't appear as a single control at all. And that means you have no access to the data behind" the control which you need to start changing it.
The only practical way to do it is to modify both applications to communicate to each other - a Socket is the usual approach.
Have a look here: Double Clicking a File in Explorer and Adding It to Your App while it's Running
] - it's not exactly what you need, but it does show how to establish a Socket as a listener, and send data to it from another application.