That's the assumption Phil made, and I made it too.
It is also important that the diode voltage drop to zero when it isn't
conducting a current. If the diode were replaced by a battery so that the
voltage was constant all the time, the RMS volts * RMS current wouldn't work.
But, *in this particular case*, it does work.
Because by pulse current, we mean a current that is on for a while and off for
a while. That's what I mean by "not constant", not that that the voltage while
the diode is conducting isn't constant *during that time*. Sorry if there was
confusion.
If you use a scope to measure the diode conduction voltage, then you only get
scope accuracy, not the accuracy you could get with a DVM.
So it does. Everybody has a DVM that can measure both AC (RMS with or without
DC) and DC current these days, I think, and the true RMS of AC+DC can always be
done by hand with the calculator that everybody also has.

Just measure the
voltage and current in both AC and DC modes and take the square root of the sum
of the squares of the two voltage measurements and of the two current
measurements. Then you get the result with only one meter.
Quite right. Then we need to use the wattmeter everbody should have, or the
really neat new 4-channel scope that does trace math that everbody wishes they
had.

!!