Atmel Studio does not give you a separate confirmation that the program was uploaded when you use the quick toolbar options. If you are just using the "Build Solution" options, that does not upload the program.
To be sure, you can go into the device programming menu that you mentioned, select the tool and connect to it, then go to the "Memories" tab and use the "Program" button to upload the specified code. The output when successfully uploading using this procedure should look like this:
Erasing device... OK
The 3pi should also restart and begin running the new code. Most of our examples start by playing a "welcome" note from the buzzer, so you should hear a beep from the buzzer when the 3pi restarts after uploading one of those examples. If you are still having problems, can you specify what program are you trying to load, and what the 3pi does once it loads?