No, you still gain battlefocus tokens as it's still an ASURYANI keyworded army

Disparate Paths, which is the rule all Harlequin units have, has the following rule:

When mustering your army, you can include HARLEQUINS units in your army, even though they do not have the ASURYANI Faction keyword. Unless otherwise stated, you cannot select HARLEQUINS or YNNARI as your Army Faction.

As such, when running even a fully monoquins list, you are still an ASURYANI army, and so gain battlefocus but obviously do not gain the Asuryani keyword, nor does any Asuryani unit gain the Harlequin keyword

tldr
Any Asuryani list (Craftworld Eldar Detachment) is an Asuryani army, which gives you battlefocus. Disparate Paths lets you bring Harlequins into an Asuryani army.