Traditionally, yes, but its declined a bit recently (more specifically the most recent game).

Genealogy of The Holy War (Japan only, SNES), Path of Radiance (GCN), and Radiant Dawn (Wii) were very story focused. They could even be pointed to as a strengths of those games.

7 (aka Rekka no Ken, GBA), The Sacred Stones (GBA), and Awakening (3DS) all have good stories as well. 7 has a very good set of main characters, Sacred Stones has a small cast that all has a chance to shine (with sections of amazing story and a great main character), and Awakening is a more light hearted story but still good.

The earlier games, like Shadow Dragon don't have much of a story.

The most recent title, Fates, promoted like it was story focused, but all three paths were just a flat out abomination (I can't tell you how ridiculous and stupid it is, you'd just have to see for yourself). However, the gameplay in the Conquest path is arguably the best of the series.

All in all, gameplay is generally the series claim to fame. However, story and character have taken an equal or even front role before in quite a few of the games, you just have to select the right one (4,7,8,9,10, and 13 all being good picks).