Yes, they are.
ATA just cleared the $1 billion mark to become a major airline within the last year or two, I believe. Alaska has been at this level for a bit longer.
In 2002, ATA has $1.277 billion in revenue (Scheduled and charter combined... scheduled is only about $890 million of it). Alaska Air Group was about $2.224 billion in revenue. Alaska posted less of a loss than ATA in 2002 ($88 million vs. $160 million).