You could use the Suica card to cover the base fare between Narita Airport and your destination, however if you intend to use the NEX, you still need to get a separate express fee ticket+seat reservation. The Suica card itself is not valid to ride on the NEX, it only covers the rails that the NEX rides on, so you still need the additional ticket.

JR tickets are broken into:
BASE FARE (the cost from point A to point B)
Express Fee (essentially the service charge to use a faster train like the Narita Express)
Seat Fee (the cost of a seat reservation, all Narita Express trains are reserved).

If you use the slower commuter trains between Narita Airport and Tokyo area, then you only pay the base fare. But trains like the Narita Express and Keisei Skyliner require an additional ticket/fee.

The Suica card will cover the base fare, but you still need to purchase a separate ticket (as I mentioned above, for the NEX, the express and seat reservation are combined into one).

So if you do want to use your suica card from Narita, you have to go through the extra step of explaining to the staff you want to use the Suica and only need an express/seat reservation.

Or keep things simple, just get ONE ticket that consists of the base fare, express/seat fee and use the Suica card later.