How exactly does adrenaline affect melee weapons' effect?

It is well known that an adrenaline shot will allow you to strike faster (hence shortens the strike speed). But does it also increase the weapon's damages ?
Since combining adrenaline and a melee weapons allows you to unlock the "Gong Show" achievement, it seems legit to wonder: is it an effect of the speed bonus, damage bonus or both ?

The Gong Show achievement is also affected by your health; if you are low on health you will not unlock the achievement. So it seems reasonable to assume that the mini-game simply checks for health and adrenaline, without having to conclude that adrenaline actually affects melee damage per hit.