Understanding use of accelerometers to measure angular (rotational?) accelerataion
Let me guess the location of the accelerometer.

My goal is to measure the instantaneous acceleration of the rod while its moving.

I will assume it's on the extremity of the rod. There would be 2 forces acting on your accelerometer:

gravity
centrifugal force

I think that you want to measure the 2nd one, of course.
Now, I can see 2 configurations depending on how you fix the accelerometer on your rod.
1. If it has the possibility to rotates (what I called floating)

Then you will have to deal with data on both x and y axis
2. It is fixed on the rod

Then you'll have only one axis data.
About your last point

let's say the rod ramps up from 0 degrees, stays at a constant velocity, and then ramps down. How should I expect the data to look like in this simple case?

I'll try to predict, I'm not 100% sure. So, in case you set-up the fixed accelerometer, you would have a ramp-up (linear, or whatever depending on the transient) to a constant value, then stays at this constant value until or ramp-down or stops.