No it's not required. But G-mail syncs contacts to your Droid seamlessly.
VZW does have the Backup Assistant service that you can use (I forget how much) to transfer your contacts from one device to another.
You can keep your hotmail account.... just create a G-mail account and sync your contacts to that... sync to your DROID and then you're done. You can sync multiple E-mail accounts to the phone. You shouldn't have a problem.