This satellite is insufficient to track ships passing through a small area. The satellite is in a sun-sychronous orbit, which means it follows the terminator between sunrise/sunset (or vice versa). So if a ship is traveling at night, or mid-day, the satellite can't see it.
I'm not sure if the Iranians have a global tracking ground station network, and if not, even if the satellite were passing over a ship in the Red Sea, Iran might not know.
Iran could put a ground station in Yemen, but the US would probably knock that out first.
Update: Iran says that it inly has ground stations in Iran, and that the satellite is only used over Iran.