Yes. You can also find out what level a Chocobo is by what enemies are in the battle with it.

Level 16 or 24 Chocobos work, since both can be hit by L4 Suicide.

Level 16s can be found around the very first Chocobo tracks, and they are accompanied by two Elfadunks (those blue Elephant looking things).

Level 24s are around Mideel, and are accompanied by two Spirals (the pillbug creatures).

Find one of those two Chocobos, use a Mimmet Green, hit it with L4 Suicide, and pick up your new Enemy Skill.