We let ours flower all the time and it is very happy. It is inside, so it never got pollinated and threw up several flower spikes over about 5 months during this last, long summer. We did not notice any change in the behavior of the plant, the rate of growth and die back of the little chompy bits (I believe that is the technical name) has been the same. We also let another of our carnivorous plants flower, a sun dew, and it is also happy and healthy.
I suggest an internet image search and you'll see what the flowers look like. Our venus fly trap put up white flowers softly tinged with pink, and the sun dew put up small pink trumpets.