Caranthir spawns a 1-power copy of the card. If you decide to use Caranthir on Imlerith, then you get 1-point Imlerith, nothing more, nothing less. If you expect to trigger Imlerith's ability while spawning it with Caranthir, then no, this is not how it works. Imlerith's ability is triggered when the "Deploy" condition is met. Meaning, you need to play Imlerith card itself to be able to trigger its effect.
This is the difference between "spawn" and "play" abilities. If the targeted card has a deploy ability, it will only activate if you "play" the card.
"Spawning" a copy (via Caranthir for example) won't get you deploy abilities, only end of turn/passive effects.