Yes you can. You might have an issue in connected mode though because while you are using Embrio the computer is communicating with the Arduino using serial.print. Your Serial.Prints might interfere with that communication, but it might not. Anyway it doesn't really make sense to use them in design mode because you can just see the data in the UI, but they do work fine in a compiled program.

On the bottom left of the screen is a serial connection control. When the plug icon is "connected" and the status is "good connection", that means you are communicating with an Arduino, and Embrio should be updating with live data. Use the little icon that looks like a microchip to upload a final program (this is only possible with a full license), and the program is uploaded to run entirely on the Arduino. This tutorial video might help.

That's a good idea! There's nothing like that yet. I guess for now you'll have put a flag in your custom arduino nodes and make sure to set the value correctly. I like the idea of a global flag so your arduino code knows if it is compiled mode. I'll add that to the list.