I have one old pc with ASUS motherboard, and i tried to change the old stock cpu-fan with another fan...
So, i start the pc, and i got the same error as you.. "CPU Fan Failure press F1 ", and after 1-2 seconds the pc continues booting normaly, the new fan is spinning normaly, the cpu temp is the same... nothing bad happens.
But, since the only reason for changing the fan was only the noise from it, and i don't use that pc often, i returned the old fan back

I thought a fan is a fan.. but i guess i was wrong.