Does Specialisation (2 points) improve damage and THAC0 of off-hand weapon?

Hi - I'm aware that an off-hand weapon does not gain any additional attacks from specialisation (in fact I think the off-hand *always* only gets one attack, unless improved hasted?), but does it still get the damage and THAC0 bonuses? It's a little hard to tell from the character sheet, especially the damage bonus.

e.g. with 2 pips in a weapon you normally get:
+1 THACO / +2 damage / extra 1/2 attack