The only "A" I'm aware of is Metro Line A and it doesn't go to Fiumicino airport. There is an urban train which does but it's outside the area that a standard public-transport ticket or Roma Pass covers. You need to purchase a ticket for a bus, urban train, or the Leonardo Express airport train.
A map of the metro/urban trains is here:
http://www.atac.roma.it/files/doc.asp?r=385
The last station on any line which is covered by a standard ticket or Roma Pass is titled in RED, so Fiera di Roma is the last station on the FL1 urban train line TO the airport which you could access without a supplemental ticket. The FL1 also doesn't depart from/arrive at Termini, if that's the closest train station to your accommodations in Rome.
As the Roma Pass website states, "all connections to and from Fiumicino Airport are not included."
An inexpensive way to get between Fiumicino and Termini (or some other stations in Rome) is by airport shuttle bus: SIT, T.A.M, Terravision or AtralL-Schiaffni. Tickets are as little as 5 euro, depending on which one you choose. They take longer than the Leonardo Express train but are quite a bit cheaper. We've taken a couple and they're clean, safe and comfortable. The FL1 urban train is an option - again, not covered by the pass - for accommodations closer to the stations/metro lines it serves.
Links for the shuttle buses:
http://www.adr.it/en/web/aeroporti-di-roma-en-/pax-fco-to-and-from
A lot of RS posters like to use cabs or car services to/from the airport, and those can be very nice when arriving jet-lagged in an unfamiliar city, and for the convenience of being dropped off right at your hotel. Fixed taxi rate to the city center is € 48,00. That cost isn't bad when you have 3-4 people to transport, and worth the splurge if you're tired and not yet acclimated to city transport systems.
http://www.adr.it/en/web/aeroporti-di-roma-en-/pax-fco-taxi