Yes, but you only add it to damage dealt. The book states that you never add STR mod to the AP of the weapon, but if you're going ot primarily Finesse attack anyway, you won't need it.
The reason I mention all that is because if you don't use a Finesse weapon to deal a Finesse attack for some strange reason, you dont' ever get better as penetrating armor because of high strength by virtue of the weapon's construction, but being incredibly accurate still won't take away from a weapon that slips through a gap in someone's jerkin being pushed deeper into his ribcage.
:shock:
I think I went overboard there with the explanation. (lol)
So...in other words...yes: Add STR mod always for damage but not ever to AP on Finesse attacks.