Does not seem to bother my Echeverias when they continue in their bloom cycle. You may be thinking about the Sempervivums. Those ones die after it blooms, so some will cut off the buds right away to slow down or stop bolting.
I know I have killed my Echeveria rundelii after it bloomed, but only because I may have overwatered it, but not because I let it continue its bloom cycle.
