if i play reckless innovator it activates his abbility?

No — playing Reckless Innovator does not trigger his "When I become exhausted" ability.

He enters play exhausted (or ready, if you paid the [Accelerate] cost), and being placed onto the board in a state isn't the same as becoming exhausted. "Exhausting" is an action that applies to a permanent already on the board (Rule 415.1), so nothing has transitioned from ready to exhausted when he resolves — the same logic that keeps entering ready from triggering "becomes ready" abilities (Rule 805.6.a).

So the ability fires the first time he actually goes ready → exhausted: a Standard Move, attacking, or being exhausted as a cost. If you paid Accelerate he's ready and can do that on your next Main Phase; if you didn't, he can't even move until he readies in your Awakening Phase (Rule 415.1.b — an already-exhausted unit can't be exhausted again). Paying [1][C] for Accelerate is the usual way to get the choice of Gold token vs. [C] to draw 1 quickly.