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Hmm, I guess the descents would mean you cool down quite a lot before restarting. I'm not sure it's high enough on my todo list to make me want to do reps of something in the Chilterns though, just figured 4x climbs of Teide would be a bit easier mentally.
You're allowed to stop on ascents though right? Depend on which climb I use I would probably just be stopping to refill food/drink on the way up at bars/cafes.
I've done it on a road bike (Kop Hill in the Chilterns, ~100m reps) and later on a fixed gear (Telegraph Hill, South London, ~40m reps).
Coincidentally, my first ever attempt was in Tenerife on the north side from Puerto de la Cruz. The long reps made it incredibly hard. Got to half-Everest then quit. Differences in temperature, no real breaks whilst climbing, logistics of food/water and storage of clothes/batteries/tools all make long reps very difficult. Short reps are by far superior if you want to successfully complete the challenge.