MySQL usually restores the entire table when adding an index, so all existing ones are also restored. It can be slow.
The only exception is adding an index using the InnoDB plugin, which does not.
As far as I know, it always performs a full table scan when creating an index, however it should do an index scan if you added an index that had the same (or a subset) of columns as another index. Such indexes are usually useful if the columns are in a different order.
Using mysql stock, the more indexes you have, the slower the new one will be, as it will also restore existing indexes.
With the plugin, I think it does not matter.
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