Is a static variable in a library (DLL) shared by all processes referencing that library?

I know that a static variable used in a web application is shared for all users across the web application. If I have a library (DLL) that uses some static private variable, do all applications using that library share the value of that variable?

For example, say I have the following code in my DLL:

private static bool isConnected = false;

public static void Connect()
{
    // TODO: Connect.
    isConnected = true;
}

public static void Disconnect()
{
    // TODO: Disconnect.
    isConnected = false;
}

Then in Application A, I call myDLL.Connect() which sets the value of isConnected to True. Then I have some Application B that does the same thing. If Application A later calls myDLL.Disconnect(), does Application B see isConnected as False because the two applications share the same DLL file with a static variable? The DLL file would, in this case, be literally the same file in the same file path.

(I previously asked a somewhat similar question about web applications here. It is not related.)