What kind of sundew do you have?
Allowing the sundew to flower shouldn’t hurt it. The flowers will make seeds if the flowers are allowed to turn into seed pods and dry. They are very, very small seeds. It depends on whether you want seeds or not. You might want seeds if you want to start more plants from seeds or if you want to donate them to the seed bank that is located elsewhere on the forum. Another reason you might want seeds is if your plant is an annual being as it will die in a year or two and you will need seeds to replant. Another reason you might let the flowers go to seed is to allow the plant to self sow, which optique cautioned about. I don’t think there’s a right or wrong thing to do with the flower stalks…it all depends on what you want.
Btw, welcome to the forum!