Do newly hatched queens always win?

[Moonshae]

If bees build queen cells that get capped, even though a brand new queen was introduced, do the newly hatched queens always become victorious? I put two frames of bees in my ob hive and added a queen, they released her and she seems to be doing fine, but they went and built 3 cells and capped them. I really don't want to waste the money I spent on the queen by having her killed in a week, but I know the bees know best and so I don't want to cut out the queen cells.

[TwT]

three things to choose from, cut out the cells,  take out the frame with the cells on it, or pull the new queen out and put in another hive, but I figure the new queen will destroy the cells herself..... you just need to watch the timing, new queens will hatch about 7 days after capped over. 

[Moonshae]

but I figure the new queen will destroy the cells herself.....

And indeed, she must have, because they've ripped down two of them today, and I suspect the third will be gone by the time I get up in the morning. I was a little worried, since they built and capped them all while the queen was there.