The situation with double ropes is complicated because we use the term “double” generically to any rope used in pairs. To break it down precisely, there are double “half” ropes, and double “twin” ropes. Most climbers outside the UK, where ratings and ropework take on Biblical complication, are befuddled by half and twin ropes, which look alike but are used very differently.
Half ropes, usually 8mm to 9mm, are used in pairs, but clipped independently to protection. These are designed to stretch one at a time to cushion the shock of a fall, just like a single rope. Clipping two half ropes to one piece doubles the amount of nylon catching the fall, increasing the impact force, just as you deduced. Half ropes are beneficial whenever you need to carry two ropes to descend, and for meandering pitches, where alternating rope clips reduces rope drag. These are popular for alpine climbing, where you need two ropes to rappel off the peak. Half ropes are marked with a “½” inside a circle on the taped rope ends. Sear that into your brain.
Like half ropes, twin ropes are used in pairs. Twin ropes are marked with two co-centric circles inside a circle, sort of like the Olympics logo. You use twin ropes, which can be as thin as 7.7mm, just like you do a single rope, by clipping both strands through every piece of pro. Twin ropes are built to work together in a sort of godless matrimony to catch falls, and are tested in CE drop towers as a pair, instead of individually like double ropes. Twin ropes offer an increased measure of security over just using a single rope, a consideration when accidentally cutting your cord is a possibility. Twin ropes are the least popular type, at least here in America.
But, it’s not as simple as that. Some ropes, such as the Edelweiss Calanques 8.5mm and the PMI Verglas, are certified as both twin and double ropes. These you can clip any which way you like, something we Americans can surely appreciate. Gear Guy has spoken!