Yes, if you practice spinning (using a higher cadence as you described the person you saw) on flats, it will be easier to climb doing this. It works for me and while I can often drop people on climbs, I think it's time to work on a little endurance... today a group of 3 pretty fast riders passed me at the bottom of a small hill I am very familiar with. I decided to catch them, which was not that hard, as they slowed more than I imagined they would. I hung with them until the top, but they shot away from me when they got to the flat. Since I was riding with people, I didn't try, but I am basically lazy when I get on the flats.
Spinning really does save your knees.

