Since in variational inference the purpose is to find an analytical approximation to some target distribution:

Once the ADVI fit has been performed via “.fit( …)” is it possible to use find_MAP(…) on this variational model?
…
I know if it was classical variational inference using a Gaussian meanfield assumption, it would be possible to find the mean of this variational distribution and therefore find the mode, which will be the MAP. This leads me to: 
In ADVI we are optimising in this transformed space, and the authors of ADVI then say: “these
implicitly induce nonGaussian variational distributions in the original latent variable space”, so the final variational model neednot look Gaussian anymore. How different can it look in practice? Can the fullrank Gaussian ADVI model, perhaps develop two small peaks in the final converged answer (become slightly bimodal? for example)