Can you make cheesecake with honey instead of sugar? Sure!
Is it as simple as just replacing it 1:1? Not quite, there's increased moisture, but check the top answer here.
You'll need to reduce any liquid you might be adding a bit. Without seeing your exact recipe, I can't give you an exact answer there.
Whoa. Whoa. Whoa....thats not cheesecake, thats no-bake 'cheesecake'. And that's not normal sugar, that's icing sugar.
No bake 'cheesecake' is much more forgiving about the ingredients - you'd not trying to set a custard like, you just want a thick, flavored, semi-firm pie filling. Add the honey, but leave off a touch of the creme, maybe 20-30 g overall? Icing sugar will actually thicken it a bit as its not only not a liquid, but its also got cornstarch in it. There's about 1/4 tsp of cornstarch in that much icing sugar, so I'd add that. If you're against cornstarch, I don't think it'd be the end of the world to leave it off.
I'd add the honey and then add 350 g of creme and see how the consistency is. You'll probably end up adding another 20g or so, but I'd wait and see.
A simple alternative would be to make a ganache flavored with Frangelico or another hazelnut liqueur. This has the advantage of having much less sugar, and probably better overall flavor, than an even-more-sweetened Nutella, assuming you start with a reasonably dark chocolate. All you do is boil cream, and pour it over a similar quantity by weight of chopped chocolate, into which you've added a healthy splash of hazelnut liqueur (or the liqueur can go into the cream as you bring it to a boil; either way works in my experience). Then stir vigorously until all the chocolate is smoothed out. You can pour it over while the mixture is still moderately warm and refrigerate it with the cheesecake. It will not be Nutella, but from experience it will be good, and evoke the same basic flavors.
Alternatively, most cheesecakes I am familiar with aren't topped with an icing, but a mixture of say cream or sour cream and other ingredients, sometimes added in the last few minutes of baking. These usually spread out reasonably well. You could consider softening the nutella in the microwave and mixing with a bit of cream, which will be a sort of less heavy ganache.
Best Answer
You can't make icing with syrup alone because it has too much water in it.
If you were planning to use the syrup in the cake itself you'd have to use more than the amount of sugar called for, and reduce the other liquid. All working by weight. Volume measurements here wouldn't work. But rather than trying to use syrup in the cake mix, it's better to use the finest white sugar you have. Many sponge cake recipes use caster sugar anyway, which is fine but not that fine.