Do Ionian islands use Piraeus like the Cyclades?

No. Visit Greece: Ionian Islands are served by Patras, Kyllini, Igoumenitsa and Astakos. Direct summer flights include CFU and ZTH.

Ionian Islands: a different sea

Corfu, Zakynthos, Kefalonia, Lefkada and neighbours sit on the west side. They do not share the Piraeus–Cyclades conveyor belt.

Visit Greece: Ionian Islands are served by Patras, Kyllini, Igoumenitsa and Astakos. Source: By sea.

Green west-coast islands, often combined with mainland Epirus or the Peloponnese.
Direct summer flights (CFU Corfu, ZTH Zakynthos, and others) from European cities — confirm on the airport/airline.
Not an efficient add-on to a Santorini week unless you enjoy extra flights.

If your ticket says ATH, you still have a mainland transfer (bus, domestic flight, or a longer ferry plan). Build the day for it.