Will landing gear with wheel fairings keep spinning due to airflow? I asked this in a side note to a previous question, but I figured it warranted its own question.

If a fixed gear aircraft is fitted with wheel fairings, even if you tapped the brakes after lift-off, would the wheels start turning again? With typical wheel-fairings I guess about one third to one quarter of the tire sticks out into the oncoming air flow, and would face perhaps 120 kts wind. All aircraft tires I've seen have grooves running along the direction of travel, with nothing going sideways that would be any obvious wind catcher, so I guess they're pretty much slicks in this regard.

Or would any 'normal' amount of friction in the bearings keep them from turning?
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.