DLC and Support. However, she's featured specially in the Summer Scramble DLC, and for some reason Tharja's the one with the Supports that reveal most of the character's backstories and other sides to them.
Most characters do not have any significance to the actual plot of FE:Awakening. The only ones that get major screen time are Chrom, Fredrick, MU, Flavia, and Bald-Headed Oaf.
and lucina, but that is more or less right. also say'ri has some parts were she talks before/after a chapter, but mainly in valm. other than that, everyone is more or less optional, but no tharja would be a massive let down. he is a very good sorc and with the right father, her daughter is as redonk OP as the rest of the children.
"Be greater than all that's come before... But... Never be perfect." - Mayuri Kurotsuchi, Captian of Division 12.