Yes. I wrote a short account of his career
here.
And if I may copy-paste from an old board:
If you read the AARs of the colonels (all in OR1, 11):
2nd Michigan - deployed mainly as skirmishers. Kearny led one of the companies in a charge! (pg 506-7)
5th Michigan - made two charges against a line of rifle pits covered by an abatis (pgs 507-8)
37th NY - on left flank, refused the flank and stood its ground (509-10)
38th NY - charged 3 times and was repulsed 3 times (pg 501)
40th NY - right wing advanced into the Slashing and was caught in a firefight. Kearny led the left wing in a charge on the left (pg 503)
So Kearny is indeed launching a whole bunch of charges, leading many of them himself. Why is he leading a company instead of commanding his division?