Well, having looked at the Initiate, I would say they do not. You could add the BAB to your current progression of monk attacks, but you wouldn't gain the lesser bonuses to your flurry of blows, nor the faster flurry attack progression.
And I think there's a Cha 15 prereq on Vile Ki Strike for a reason. If it had a Wis 15 prereq there would be no reason for a vile monk not to take it. You need to take some sacrifices for this feat, as vile damage is no walk in the park.