Will landing gear with wheel fairings keep spinning due to airflow?
This is a very general question. So the answer is:

Sometimes they spin, sometimes they don't.

Have you ever seen a car with a bicycle on a trunk rack, and the front wheel is spinning. Sometimes they spin fast, sometimes slow, sometimes not at all. It just depends on the air flow.

Airplane wheels are the same way, and it all depends on the airflow, the tires and the bearings. The airflow over tires sticking out from wheel pants is going to be turbulent and unpredictable. Sometimes it happens, sometimes it doesn't. I've seen both.