Yes, your router should have the 256 IP addresses on the Internet interface of the router.
But with MikroTik RouterOS being so poerful, you could do it the ordinary way and directly route the Internet and your LAN. This is if your LAN has the internet real IP addresses set. If you don't want to reconfig all puters in the LAN and set them IP addresses than what you're trying to do seems right. Good luck
BUT Couldn't MT reply to arp requests without having to set all those IP addresses ? And together with both-ways NAT to be able to do the task ?
Set up a Bridge, in Bridge->NAT - set up an arp-reply with routers MAC for all IP addresses (or the range if possible). Not sure if this will work... don't know much about ARP and how the hell MT handles it.
AArgh why why why why why why must it be so hard and so inhumane this GUI or whatever it can be called - winbox and console... There is not enough info wich does what., not even with the manual, MT is way too powerful but maybe only the military are entitled to know how to use it.