A pomegranate martini is supposed to be sweet...vermouth would just kill it.
I'd say yes, make it like a Cosmo, but instead of using triple sec (which is what most Cosmos call for) use a better orange-flavored liqueur like Grand Marnier or Cointreau (both of which will cut the sweetness and add balance to the cocktail).
Personally, I think good cocktails are about finding what works for you. So get some good ingredients (POM, actual pomegranates, Grand Marnier, simple syrup) and make a lot of different kinds of pomegranate martinis until you find one that fits YOU. Then you have a signature drink you can make for all of your friends as well
Also, it's not necessary to juice the pomegranate: treat it like you would a fresh lime or lemon when making a cocktail. Get a shaker, put the pomegranate and ice in the shaker, and muddle it with a muddler (if you don't have a muddler a wooden spoon works just as well usually, especially with ice as it helps break things up a bit), then mix your cocktail. Use a good, bar-quality strainer to strain the drink into your martini glasses.
There are tons of ways to use pomegranate in making cocktails. Have fun with it.