What could possibly happen? We think you should go to jail! Cheesecakes are not to be trifled with. Plain or chocolate are the acceptable choices, and chocolate should be made infrequently.
Alas, ours is not the only opinion on the subject. Indeed, Stephen Wheeler, your apparent soul-mate, provides a no-bake recipe in The Book of Cheesecakes (Canada, UK) that is going to make you cry - it includes pink and white marshmallows. Mr. Wheeler asks you to combine 12 ounces of marshmallows and 1/3 cup of milk in a pan and blend them over low heat until the marshmallows have melted (a double boiler would work well). Allow it to cool.
Beat 1 pound of cream cheese (he uses American Neufchàtel, which is a somewhat lower-fat cream cheese) with 2 tablespoons of lemon juice and then add the marshmallow mixture and beat until smooth. Whip a cup of whipping cream, and fold the whipped cream into the cream cheese mixture. Add pink food coloring "until the desired shade is reached" (the man has no shame!), and spoon it into a prepared crust. Refrigerate for 2 to 3 hours until set. He also wants you to garnish the thing with marshmallow halves in a border around the edge (alternating pink and white, of course), and suggests you drizzle a little melted semisweet chocolate here and there across the top, as well.
You can certainly also experiment with marshmallows in a traditional baked cheesecake recipe, but we can’t give you much guidance, as we seldom bake with marshmallows. They are basically sugar/corn syrup, a gelatinous substance, and air. You don’t have to worry about the air, because that will dissipate as you melt the marshmallows before adding them to the batter. How much sugar you should displace with your marshmallow fluff will be a matter of experimentation. A given volume of marshmallow is going to be less sweet than the same amount of sugar, so you might opt to eliminate some of the sugar, but not all.
The biggest variable we see relates to the effect the marshmallow will have on the body your cheesecake. It is going to stiffen it substantially. Rather than leaving some sour cream out of your recipe, we think you might want to find ways to add a bit of liquid to the batter, or the cake may come out more rubbery than you’d like. Another option is to cut back on the eggs, as they are what sets up as the cheesecake cooks and are primarily responsible for the transformation from batter to cake. Reducing the sugar and eggs and adding melted marshmallow may give you the taste and texture that you’re looking for.