Nah, I think just bending up and down on a chair could make more damage than good, it puts strain on your back and don't do much for your belly (as I guess the intention is). As a back-stretch, that would work fine just bending forward and resting there.
But, you can get a similar effect as sit-ups from sitting with a straight back and lifting your legs up and down. It does exercise your thighs a bit more than it does your stomach, but it still has an effect. Alternating between bent and straight legs will also activate different muscle groups.