The actual bad sectors are a property of the physical material in the drive, and are not copied. In other words, if you have ten bad sectors on hard drive A, and five on B, and you clone A onto B, B still has exactly the same five bad sectors that it did before the cloning process.
I would assume that the hard drive itself (or any checkdisk-style process run on the drive) will map those sectors elsewhere so that the cloning software doesn't try to write data to them, but that has no impact on the actual bad sectors present on the drive, and doesn't change the answer to your question.
You do have one problem, however. If the hard drive you're trying to clone has lots of bad sectors on it, then data may have already been lost. So you're probably better off reinstalling anyway, and moving your data over afterward.