Hello Ivan,
There is not a direct way to calculate the average power of the on period of a pulse, but using what we do have, if you notice in the AM vs Time plot in zero-span, there is an average power readout(in newer versions) which takes the average power of the entire acquisition. If you set your trigger position to 0-1% and acquisition length to the length of the pulse, this would give you the measurement you are looking for.
I will add this measurement to our request list, and determine if there is a way we can accomplish this more easily.
Let me know if you have questions or comments.
Regards,
Andrew