Potatoes only came to the SC in the 17th century....and that was only along the areas under Portuguese influence (i.e western coast). Biryani was being cooked and prepared way before that...so its safe to say that originally no aloo involved.
But...i guess the same argument can be made for tomatoes and chilis too, which are now staples of North Indian/Pakistani cooking.
But here's one interesting thing, if Potatoes were brought by the Portuguese, the western coast areas, especially Kerala (malabar - WHich had the 1st Portuguese contact) and the Konkan (mumbai, goa, karnataka) areas, (which have significant muslim population) never used "Aloos" in the Biryani (malabar Biryani, Hyderabadi, Donne styles etc) . Though we use them in a lot of other foods.
But w.r.t Chillis and tomatoes, what you said holds true.