Choosing a distribution with GEE methods

I've just recently been exploring Generalized Estimating Equations for use with my data. I know that QIC values can be used to evaluate which working correlation matrix is most appropriate given a particular distribution and model, but I'm curious whether one can use QIC values to determine which distribution is most appropriate?

For example, could I compare root transformed data (using a normal linear distribution) to just using non-transformed data with a gamma distribution with log link, to a tweedie with log link distribution simply by comparing the QIC values in the output for each model?