Do you know how horrid iOS 7 would run on the iPad 1? Sure it would run, but it would be like running Windows 7 on a Pentium 3 with 256MB of RAM and a 10GB hard drive on a ATA/33 bus. Completely awful. And before you say it, no the iPad 1 is not that similar to the iPhone 4. The iPad 1's GPU has to work much harder to drive more pixels, something that iOS 7 heavily taxes already on the iPhone 4. It's ram is half that of the iPhone 4's with the iPad 1 already being the most ram deficient of all A4 devices, due to its large screen. The only better thing is its CPU, but that isn't enough to make up for its overall extremely poor performance. Even when compared to the iPod Touch 4 and iPhone 4 all running iOS 5.1.1, the iPad 1 was the overall worst performer with the 3Gs beating it out in everything but raw CPU related tests.
I don't know how it would run because they never released it. And I run windows 8.1 on a 2004 HP celeron with a 1.6 single core. Is it super fast? No. Does it function? Yes. Video games do it all the time, they have settings for lower spec machines. Is the experience exactly the same? No but again I'm talking functionality. Give me the choice to upgrade to iOS 7 with features stripped out. I'm sure it can handle something so I can upgrade my apps. As it sits my chrome doesn't update so I can't use the sync feature do to a bug, hell my IMDb app won't upgrade, I'm sure that taxes the system. Netflix works and I'm sure that's more taxing than a new notification bar and some new icons.