Absolutely, nope 👎.
The MRT line from the airport to Taipei Main station is being managed by a different company named Taoyuan Metro 🚇. You can’t use the Taipei Fun Pass card.
To ride the MRT to Taipei Main Station, just proceed to the station, then buy a token from one of the vending machines for 150 NT. It’s very easy.
If you have thousands with you, use this machine to exchange them for smaller bills.
Currently, the station at Terminal 1 and 2 opens at 5:45am.