A level 18 Pixie Barbarian

[visigani]

Would this be considered an Epic Character?

[Kennisiou]

Assuming you haven't bought off the level adjustment then yes. Even if you have, it may require epic or near-epic amounts of EXP to achieve.

[Urpriest]

With respect to what?

If you mean for qualifying for Epic feats, ECL is what determines that, yes. That's made pretty explicit, page 209 of the DMG for example lays it out.