No. The term Elder Dragon only refers to those that originally arrived and settled on the world of Ith, so the first dragons used by the Dragonier were not Elder Dragons.

The thing you're missing is something I haven't mentioned yet and I'll explain it in more detail later on, but the gist is that if there were enough dragons to sustain their immortality then they'd live and grow indefinitely until they became as big as the Elder Dragons themselves, so that's basically their final form. The tradeoff is that they lose the ability to reproduce after a certain point, but none of the first dragons born on Ith got that far by the time the first Dragonier rolled around, so it's all academic.

As for where the first Ith born dragons came from, they were carried over as eggs by the Elder Dragons. They're the ones all present day dragons are descended from, so I guess it's a bit misleading to call them 'spawn' of the Elder Dragons, but also technically correct(?) idk, I'm sure there's a better word for it, but it's all I could think of at the time. Anyways, I hope that about covers it.