Yes. As far as I know that is true of any plant. Not to be a wiseass, once something is dead or well on its way, it is not coming back. Leaving blooms, branches, stems, etc. that are not growing could well be slowing the rest of the plant down. Those things are going to grow much, much bigger. You can easily remove 15-20% of the above ground parts every year and not oly be fine but probably help the plant. My $.02. I understand your concern but encourage you not to worry. Good luck.