You would need to customize the:

New Products link in the Categories sidebox
What's New Sidebox
New Products Centerbox
New Products Listing

To not show when the customer is not logged in ...

Then you would need to add a filter or exclude to the where statements on all the other functions of the site to prevent New Products from showing in Featured, Specials, Product Listing, Product _info on Prev/Next etc. as well ...

After you have customized all of the code everywhere ... this should work for you ...

In other words, it would require a heck of a lot of code to prevent guests from seeing new products ...

It can be done, but it is a lot of work ...