You get an additional 3 from the NC itself (so 4.5 with the NC modifier). A total of 12 in your example.
Liberty should still go for it in a reasonable amount of time.
Ahhh yes I forgot about the 3 science from the NC. But yes you're right you don't want to delay it more than necessary. The key thing is to keep your population growing as much as possible in the meantime. If you are in the top 25% percentile for population in the demographics then you're not going to be suffering from lack of science too much. Early caravans can help out a lot here too with science but their value diminishes in time.