We haven't had the chance ( woo-hoo) to do that yet. Down in So. FLA there are not that many copper gutters, as a matter of fact I can't recall seeing any at all.
I have a house I have washed 3x and the roof once in a five yr period. No discoloration or other problems to date.
As long as the gutters aren't clogged and spilling over the only possible discoloration if any, should be on the inside. A careful sauce application w/good rinse and you should be fine. I wouldn't lose any sleep over it
I would assume you will be ok reggie. Most copper gutters have a clear coat finish on them to keep the shine. If this is true then rinse and flood brother. Git er done! Reggie be sure to get your signature block filled out also in the User CP tab.