Email Fowrarding Question

I tried google but no answers so I try here.

I have email forwarding setup on my server. Eventualy each user will have their own private something@mysite.com email which simply forwards emails to their home / personal account. There is no actual email account so no login send recieve capabilities.

But my question is does forwarding emails eat up my transfer data? Im sure some amount of data is used up but not the size of the email? Or is it?

Thanks,

Dave