I know you understand the difference between current, time and energy. If the configuration requires more time than the run duration, then it is only reasonable that it will consume significant energy. Using the current values above of 200 mA for configuration and 1000 mA for running with my numbers of 100 ms for configuration and 10 ms for running, the configuration would clearly take more energy than the processing.
Of course none of these numbers are real, but they are realistic. The point is it depends on the application.
Your example is not complete and of course it matters.
To be honest I don't get what you are describing. I thought we were talking about a situation where the device was powered down to save energy. Yes, looking back, that is what I said. When there is something to process, the unit would be powered up and the FPGA would have to be configured. This configuration energy is a product of the current and the configuration time. You seem to be talking about something different and completely ignoring the time issues.
Regardless of whether the configuration current is a hundred amps or a microamp, if the duration is long enough the energy becomes significant. At a first order of approximation, the configuration energy is significant if the application current-time product is a factor of 10 or less greater than the current-time product for configuration. In other words, the configuration energy is less than
10% or so. There may be applications where the energy wasted in configuration is even more critical as the battery margin is less.Are we talking about different things?