Just did a quick test
Custom battle set to VH, grassy plain, AI controlling a unit of Gaelic Archers (missile attack 7) recorded below the number of kills after archer fired 10 arrows.
The test was done first a Night to force the AI to use flaming arrow. Then repeated at Midday for normal arrows

Noble Pikemen - Unit size 76, Armour 7(upgraded), Defence 7, Shield 0

Night attack 15, 12, 25, 22, 20, 19, 21, 17, 23, 14 = Avg 18.8
Midday attack 33, 25, 26, 31, 26, 25, 27, 32, 32, 24 = Avg 28.1


Highland Pikemen - Unit size 76, Armour 0, Defence 6, Shield 0
Night attack 39, 37, 45, 53, 43, 35, 43, 39, 50, 47 = Avg 43.1
Midday attack 44, 57. 62, 67, 59, 55, 61, 64, 54, 52 = Avg 57.5

The number of kills per 10 arrows is higher for normal arrows, than for flaming arrows, on target with or without armour.
In addition the rate of fire for normal arrows is about twice of flaming arrows.
If the battle was allowed to continue the Noble Pikemen unit would route only after >70 men had been killed. The Highland Pikemen routed after >60 had been killed.

There is no indication that faming arrows have any advantage against armoured units

My archers will continue to draw normal arrows for both night and day battles.