Matching LPC frequency response to raw sample data frequency response
Is using the coefficients directly as input to the FFT the right approach?


It depends on what are you going to do next. There are many formant extraction algorithms, you can find recent advanced one in COVAREP https://github.com/covarep/covarep/blob/master/formant/formant_CGDZP.m


  and perform FFT directly on the LP coefficients padded with zeroes. 


It seems like a crazy step with not much meaning. Why are you doing this? LP coefficients create very rough spectrum approximation, the rest is in residual, but FFT from LPC, it is something strange.

Windowing does not change much, the difference will not be visible. You only can get a few percent more accurate results from it.