Yes, if it's less than 24 hours, you will be allowed to do a stopover using an F award ticket. We added a fabulous night in SFO to our recent F award trip to Japan.

You may be aware of this, but I'll mention it because it's a difference between a short layover and an overnight stopover: For a stopover of this length, you will be required to claim your luggage, then recheck it for your onward flight.