Are there pitfalls in using the output of machine learning model, such as a neural net as the input to a traditional GLM or similar?
Theoretically there is no problem. I've seen tree models put as predictors in logistic models. NN as input into a GLM moodel makes sense. The ultimate decition should be made based on the predictability of the NN.   

You have to mind a few issues:  


model mantenance and deployment. The NN model would probably have more parameters than your vanilla GLM deployment might be more involved. You could live it frozen and never update it, and let the GLM model use the NN score as long as it adds to the GLM prediction.  
interpretability. There might be managers whose acountability is to review risk, and they may not be comfortable with a NN. In that case feeding the NN results into a GLM might make it more acceptable, much as credit scores are used in some risk models.