I thought I'd post my experience to the collective. Mine is a bit different as I accidentally added a 3rd punch.
My initial algae outbreak was due to not realizing that once my CO2 runs out I can't just run the lights and ferts like normal for 5 days before getting the tank refilled. Finally getting the CO2 running again slowed the growth of the BBA and staghorn, but after 4 weeks i couldn't take it and perfomed the 1-2 punch per the originally outlined 4ml of peroxide per gallon...i was taking no chances on not killing everything. Livestock included 2 cardinal tetras, a cory, 3 amanos and tons of ramshorn and MTS snails (very low bioload for a tank this size).
Anyway, apparently I did not realize that I had a CO2 leak. 2 hours after completing the treatment I ran out of CO2 again. I ceased ferts and turned off the lights for the 4 days it took before I could refill the tank and solve the leak issue.
Adding the 4 day black-out (the 3rd punch) may or may not have contributed to eliminating the algae, but I think it hurt a few of my plants. My blyxa had been doing great and it almost completely died..I have a few small sprigs left that I think are recovering. My Pogostemon Erectus was similar. The lower portion died, but I've replanted the tops and they seem to be recovering. All my Bacopa and hygro varients were completely unphased.
I did lose 1 cardinal, but he was very old and had looked terrible for nearly 6 months...I was planning to put him down anyway. I also lost a ton of the ramshorns, but interestingly the MTS were fine.
Overall I would call it a success. I am considering just adding this to my normal process every 3 months or so when I need to clean out the canister...though I will likely cut the peroxide dose in half unless I have another major algae outbreak for some reason.