MX Record Question When Changing Host

I have a basic question about e-mail. I have one domain which has e-mail through everyone.net. There's no web hosting. I would like to transfer this domain to a reseller host. The DNS is hosted externally at mydomain.com, so I could add an MX record pointing to the new host. If I gave it a "0" distance, would this result in the new host's e-mail servers picking up the e-mail as soon as the DNS servers of the world are updated? If I am understanding this correctly, at first e-mail would be handled by everyone.net until the DNS servers of the world are updated. Would this result in e-mail spread over two servers for about a week?

 

 

 

 

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