Wait a second. Do you actually keep "surfing" down it for miles?? I thought that was only done near shore where waves break. If so that's the most amazing thing I learned this year yet :-)
Since it looks like you might not be getting an answer - I can't speak to ocean waves but I strongly expect so. I've certainly surfed non-breaking standing waves in whitewater just fine (not me, but e.g. https://www.youtube.com/watch?v=OlwijfFpk3E)
Surfing is just sliding down the rise in water caused by a wave at the pace as the water rises behind you as the wave moves (in the case of standing waves, I mean moves relative to the reference frame of the water).
Yes you do. The teams that typically win the Molokai'i Hoe (the race between the islands) are the ones that ride the waves the longest. You'll stay on the same wave for 20-30min if you're good.
Surfing is just sliding down the rise in water caused by a wave at the pace as the water rises behind you as the wave moves (in the case of standing waves, I mean moves relative to the reference frame of the water).