From CIA airport yes, it’s part of the public transport network.

From FCO airport, no. It’s only served by Trenitalia and Leo Express I think.

• Free use of the city’s public transport network for 48h from the first validation on the means of transport. It is valid on all means of local public transport operated by ATAC (bus, metro A, B, B1 and C and railway lines Roma-Lido, Roma Flaminio Piazza del Popolo-Viterbo, Roma-Giardinetti), within the territory of the Municipality of Rome. ATAC Bus line 720 to connect Ciampino Airport to Laurentina Station Metro B and the ATAC Bus line 520 to connect Ciampino Airport from/to the Metro A stations of Subaugusta (bus terminal at the square in front of the Metro stop) and Cinecittà. Must be completed in its entirety and is not transferable. The card must be presented at the request of control staff, together with a valid ID. All special connections tpl Atac, the railway lines Trenitalia FL, the connection Tiburtina/Termini/Fiumicino Airport, the connection Trenitalia “No stop” Roma Termini-Fiumicino Airport (Leonardo Express) and all connections to and from Fiumicino Airport are not included.

https://www.romapass.it/en/the-cards/

Thank you so much for your response. Understand that Tiburtina/Termini/Fiumicino Airport train travel not included in Roma pass. Thank you once again

No problem. 

The Wikitravel page for Rome has a good summary of the options from Fiumicino to Rome.

https://wikitravel.org/en/Rome#By_plane