shallots and seed tops (could apply to onions)

My experience with the onion family is just chives. They all have beautiful lavendar seed tops. I'm trying to grow shallots this year. I planted the bulbs in March (zone 6b) and they are growing beautifully. They are all producing seeds on their top stalk. I don't want the seeds to fall into my limited vegetable gardening area. Would it hurt the plant and the crop if I cut the seed tops off?
On another note, I have 3 onions that I didn't harvest last year and they have grown enormously with, again, seed tops on the main stalk. If the seeds fall, won't onions grow from those seeds?
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