You don't have to put a finish on it - I have varnish on one of mine to keep the dye on, but that is the only reason I can think of to put any sort of finish except for protecting the engraving, which probably isn't necessary. I do believe that some of the old scrimshawed horns were shellacked to protect the engraving (I presume...)One thing I have found is that the varnish scratches easily, which might be a consideration.
Incidently, unless you have a really exceptional horn, you will end up reshaping the horn to get the lines to flow properly - which means you will be sanding it A LOT. Or, once you are done with your rasp, you can use your pocket knife to scrape it with. A scraper cuts as fast as 60 grit and leaves a surface like 220 grit, which you can polish further with wet-and-dry if you like. I'm partial to the scraped finish myself...
Oh, and if you have a drawknife handy you can use that for shaping before the rasp. Works really well - I love my draw knife.