Aye, that's correct.
Fire Emblem is pretty good. The paranoia of losing a soldier forever is both a good and bad thing though, because while it makes it more realistic, difficult, and unique, I feel it adds a bit too much worry to the game. It's not a big deal, though.
Either way, if that issue with a unit permanently dyin' does ever become a bigger deal for ya, you'd be happy t' know FE12 (Heroes of Light and Shadow) has a "casual" mode where fallen units return t' fight with ya next chapter.