Is it necessary to empty the ablution water and refill it if drops from the hands fall into it at the start of ablution?

Washing the hands before ablution (wudu') is a Sunnah (definition) (recommended act), not an obligatory one. The water used in this washing does not become musta'mal (used/impure) because it was used for a purification that was not obligatory. Therefore, it is permissible to perform ablution with it. If a small amount of water used for removing ritual impurity falls into the vessel, it does no harm.