Hardly… Pakistan will do whats in its best interest. If strategic depth means preventing Indians from using Afghanistan to undermine Pakistan interests, then is more then reasonable to assume Pakistan will do its best to prevent such an outcome.
And lets not beat around the bush. Indians are just as involved in Afghanistan as any other country. Their aims may be different, their jargon may be different, but Indians are jostling for influence as much as Pakistan.
From Pakistan’s perspective, Afghanistan is strategically to important to simply ignore.
As for the stratgic depth of the Afghan Taliban, I doubt you have much credibility to make such a broad statement. The CIA can only conjecture on the extent of the Talibans reach or strategic depth in Pakistan. I think you underestimate the complexity of the problem. This after all is not Indias domain of influence and never really has been, so I doubt India or Indians have any genuine input on the situation.