I'm trying to model sequence data that has 5 hidden states. Observation data conditional to each state is gaussian except for one state for which mixture of 2 gaussians seems more appropriate. Unfortunately, the R package that I'm using (depmix) does not seem to support (without extending the package) a GMM as a possible response distribution. So I was considering the possibility of adding a 6th state so I could interpret one of this enriched set of states as a state for which observation distribution is the first gaussian in my above mixture and another one as a state for which observation distribution is the second gaussian.
Am I wrong thinking that the two approaches are equivalent?