Honestly, if the series ends with Don adopting some new identity I think it would make more sense, and frankly be a better ending if it ends with him saying to some person he’s just met, including say a ticket agent, “Hi, I’m Dick Whitman” and have it end there.
The proposed theory strikes me as just way, way out of character for the show.
Mad Men has never been about shocks, or twists.
If anything, the theory reminds me of all the people, I’ll confess to being one, who had elaborate theories during the first season of True Detective who were convinced there was going to be some supernatural ending to the series and clearly wound up reading far, far more into the series than the writers intended.