Depends, if you look at plants in the natural world they produce seed and continue to thrive. Gladiolus aren't different it's up to you. If you remove most of the flower heads and seed pods and let a couple develop the plant will be fine and you'll have more than enough seed to get a few plants and see what they look like in a few years time.
I deadhead a lot of plants 1) to keep them looking tidy 2) to encourage a further flush of flowers 3) I don't want to have them taking over the garden and have to spend hours pulling up unwanted seedlings from everywhere.
I collect seed of some salvias and other plants so i have plants for next year or to give away.