BRB p. 67 (Armour Piercing): "Wounds caused in close combat by a model with this special rule (or who is attacking with a weapon that has this special rule) inflict a further -1 armour save modifier, in addition to those for Strength."
BRB p.66 (Always Strikes Last): "If a model has both this rule and Always Strikes First, the two cancel out and neither applies so use the model's Initiative."
However, this only applies when they actually are using the GW, and does not mean they would somehow benefit from having ASF a second time from another source.