Here's my amateur's analysis of the situation.
Even if you did not add the Ischia culture to the IDY-based poolish, and you kept feeding it, at some point it would be likely that your local wild yeast, whatever its source(s), would take over the IDY-based poolish. The reason is that the local wild yeast would eventually produce acids in quantities in which the IDY would not be able to survive. I suspect that as the IDY cells died off, they would be consumed by the local wild yeast. I think they call this process "autolysis", or something similar.
Now, with the Ischia culture added to the IDY-based poolish, at some point, there may be a battle between the local wild yeast and the Ischia strain of wild yeast. For a while, until the IDY dies off, the IDY and the local wild yeast and the Ischia wild yeast may co-exist, but once the IDY is gone, that is when the battle between the two wild yeasts is likely to occur. Given enough time, and enough feedings, maybe one of the wild yeast forms will overtake the other. I don't know how long that would take, or how many bread or pizza doughs you would have to make with the two poolish (the IDY with the Ischia and the Ischia alone) in order to make taste comparisons.
If my analysis to this point is correct, you might have saved a step by making a poolish with your local wild yeast and adding some Ischia culture to that poolish. At some point, you would end up making doughs and crust comparisons with the local/Ischia poolish and the Ischia poolish by itself. If both crusts taste like Ischia crusts, then maybe that would be evidence of the ability of the Ischia culture to retain its inherent characteristics and dominance over your local wild yeast.
I look forward to your results with your experiment if only to see if they tell me that I am still an amateur or not.