Generally speaking, how long does it take to clear customs and immigration at the Rome Airport at 11:00am?
There is really no customs clearing. You simply walk out of the baggage claim area through the “nothing to declare lane”. Occasionally the customs officers (Guarda di Finanza) might random check someone but it is so rare that in over 50 trips to Italy from abroad I was never stopped.
There will be a line before that, upon disembarking, called PASSPORT CONTROL. Since I go through the EU citizen line I have no line, but the non EU line varies in length depending on various factors, mainly how many international ,flights arrive simultaneously. Lately they have installed e-gates where you scan your passport and take a picture before the automatic doors open for you to go through (those e gates are both in the EU line and non EU line), therefore the lines should go faster. I would plan for at least one hour, not because of passport control but because of baggage claim. That is the place where I often have to wait longer.
But if you are planning to book something (train or tour) upon arrival, know that the most likely reason for delay may not be passport control or baggage claim but flight delay (for weather, air traffic, or other reason) and nobody can predict that.