No responsible surgeon can answer this question without knowing more information about you and examining your nose first.
Whether alar base reduction can affect breathing has to do with:
1) Starting width and circumference of your nostrils
2) How much reduction is necessary
3) Whether its an alar flare reduction or an alar sil reduction or both
4) Whether the surgeon's incision is going to penetrate the vestibule of your nose and make the actual hole smaller too
5) whether you have nasal airway obstruction to start with as well as the condition of the septum and turbinates which could also be adding areas of obstruction to airflow
If the nostril hole is going to get smaller then its purely physics and math: a smaller hoe will provide greater obstruction to airflow. Simple as that.
With that said, I have never had a patient subjectively complain of nasal airway obstruction after nostril reduction but im sure objectively there would be less airflow.
Web reference: http://www.virginiarhinoplasty.com/