It has happened here, too

[ElvisLives]

First Fair Catch Kick in NCAA has happened. Montclair State vs Lycoming. Lycoming punts from their end line, Montclair State makes fair catch at Lycoming 30. Montclair State misses 40 yard Fair Catch Kick as time expires in the first half.

Total points scored on Fair Catch Kicks in NCAA and Texas high school football = 0. 😂

[Morningrise]

Things to remember for when it happens in your game this week:

• The clock ran to 0:00 after the punt. The crew correctly restored 0:01 to the clock. Make sure the coach is aware of this, as it gives him the option to run a play from scrimmage instead.
• The clock did not run during the fair catch kick. By rule the clock should start when the ball is kicked. The crew correctly took the time off the clock and ended the half.

[ElvisLives]

Things to remember for when it happens in your game this week:

• The clock ran to 0:00 after the punt. The crew correctly restored 0:01 to the clock. Make sure the coach is aware of this, as it gives him the option to run a play from scrimmage instead.
• The clock did not run during the fair catch kick. By rule the clock should start when the ball is kicked. The crew correctly took the time off the clock and ended the half.

Yes.
Regarding the clock running during the FCK, the GCO must wait until the R signals for the clock to start. So, if it didn’t run, the R probably failed to signal.
Everybody have a great game, and stay warm (in the low 50s here right now).

[bctgp]

If the fair catch occurs as time expires in a half, the team still has option to make the Fair Catch Kick as an untimed down.​ 

[ElvisLives]

If the fair catch occurs as time expires in a half, the team still has option to make the Fair Catch Kick as an untimed down.​

In which case, the R would not signal for the clock to start when it is kicked.

[ncwingman]

In case anybody is curious, here is the video. It starts with the punt/fair catch through the FCK.