No. Without going into spoilers the Dark Urge has nothing to do with the tadpoles and it never did. Also based on datamined info it seems like the Dark Urge was originally intended to be the base Tav experience regardless of tadpole use. It's more related to the plot of BG1 and BG2 than tadpoles. That's why it seems like like the Dark Urge is literally Tav+ or rather why Tav seems so bland and empty.
The Dark Urge was alluded to in the original illithid dream sequences but it tried to turn you against the dream visitor. So yes, it was baked into the regular Tav but it was also only "unlocked" if you used the tadpole.