Yep, Matparise, my Irish Tours would do the tone from that Kotzen clip with the right amp set up. My strat (rosewood board, alder body) isn't quite as "clear" sounding as that, but it's got quite a thick tone accoustically anyway.
I am thinking that possibly even slightly lower - Mother's Milk, like you say, or Apaches, would get you there more easily, letting the amp/pedal put the dirt in. I've only tried the Irish Tours myself though :D