What does this do? Is it a choke?

 

It is sort of like a choke, but designed more with fuel efficiency in mind.
There are 2 sets of butterflies in the DPFI throttle body.
The lower one is your throttle plate for acceleration.
The upper one is for the tandem function. It isn't a full butterfly as it has a cut out to allow air through. It redirects air around the injector for a better mixture rather than restricting air like a choke does.

 

I'm missing the 12v on the black and yellow wire. If this wasn't working correctly, could it effect my O2 sensor?

 

Probably at high RPM.
Drivability will also take a hit as you will be losing power.

 

It caused my car to surge when I tried to accerate. I zipped tied it open until I can get to the troubleshooting this weekend. Will his cause any problems?

 

It shouldn't cause any big problems.
I have read that it reduces power at low RPM to drive with it open.