Birch sap does contain sugar but not a lot. You have to boil 100L of sap down to get 1L of birch syrup (while for maple syrup you only need to boil 60L down to get 1L).
Fermenting the sap directly you're not going to get much of anything, probably less than 0.5% abv if you don't add any other sugars. I know you said you are going to add sugar, but I do wonder if you'll be tasting much flavor from the sap at all if you don't concentrate the sap.