Dear Gentle james,
Welcome back to the Wefugees Community and thank you for your question.
Unfortunately, the duration of the asylum procedure and the times you were holding a "Duldung" (temporary suspension of the deportation) can not be "counted" in terms of the requirements for the naturalization procedure. The law is asking the applicant to prove a "legal and continous/uninterrupted residence" (the Duldung is not considered as legal residence, as the person is de facto still obliged to leave the country) for a minimum period of 8 years. However, please note that you can shorten the period to 6 years if your German language level is better than B1 (or 7 years if you successfully completed an "Integrationskurs"). For more information you can check also this thread as well as this website (tailored for applicants residing in Berlin though).
I hope this helps and don't hesitate to get back to us with any further questions.
All the best,
Meike