Does Ekko, Revolutionary activate Legion with his ability?

No — activating Ekko's ability isn't "playing a card," so the activation alone doesn't turn on Legion. Legion checks whether a card has been Finalized by you this turn (Rule 812.1.c), and an activated ability with no card attached never satisfies that, same as tapping Darius (FAQ #2876).

One thing worth flagging though: the ability's resolution does play him — "Banish me, then play me to your base, ignoring my cost" is a played card (Rule 420.3), so once the ability resolves, Ekko counts as a card played this turn for any Legion abilities on your other cards going forward. He can't satisfy his own Legion text with it (Legion wants a card different from the one with the ability), but he doesn't have any anyway.

Also, the [Action] tag on the ability is just timing permission (Showdown–Open, any player's turn) — it has nothing to do with Legion.