NLTK's strength is the clarity and flexibility of its code, for when you're experimenting with various processes and representations to find out what works.

If you have a single NLP model that already works, you wouldn't gain anything from rewriting it using NLTK. It would probably just get slower, because you're adding abstractions that you've already shown you don't need.

I say this as a fan of and (once) contributor to NLTK.