Technically, yes. More accurately it uses the same D3D device PS2 is using. Unfortunately more than likely OBS will perform a similar hook that we are and intercept the DirectX calls prior it to reaching the tracker. Meaning you will see the overlay, but your viewers won't unless you run in Windowed / Full-Screen windowed.
This is what the streaming overlay is for. You can always configure the streaming overlay to only display achievements/killstreaks as well if you want it to match the in-game version.