I don't think it's unfeasible if the Persians manage to subjugate both the Phoenicians and Greeks such that they can build up a naval tradition within the Achaemanid state; from that point, the easiest ways to wage war from a logistical standpoint are going to be tied to the seas rather than marching south/west from Egypt or north from Greece into the Balkan tribes.
I'm imagining a scenario where the Persians set out to subjugate the Greek cities of Southern Italy, and end up building a fleet with which to transport and supply a land army, as well as levying ships from their tributaries to east to engage the ships of the Italian peninsula. Seeing the value of the fleet, the Achemanids begin a pet project of sailing around the Mediterranean and establishing a very loose suzerainty over the cities, statelets, and tribes of the Mediterranean to the point where the Persians are the incredibly loose overlords of most of the Mediterranean. No real governance, simply tributaries, but a Pax Persica is established across the Mediterranean due to the Persian's domination of the seas, such that no other naval powers exist in the Mediterranean.
It's interesting to image a scenario where Persian strongholds are set up in Malta and other minor Mediterranean islands that could lead to pockets of Persian speakers once the Achemanid Empire collapses.