Will it be a problem? Yes of course?
Do you plan on leaving the original server there as a primary nameserver for all of the accounts you are transferring?
Or, when you transfer the accounts (if via WHM's function), the zones will be created on the server you are moving to. As long as the zone configuration is somewhat sane on the new server, you should be able to get away with that nameserver powering the zones for the domains that were there, and the new domains you're moving there.
And finally, you can transfer the nameserver host from the original server, to the new server, provided there is a free IP on there that doesn't have a nameserver host bound to it.