If you do end up doing it definitely commute on the train, it will make it 20x less painful.

Even then I spent last year alternating weeks between DC and NYC. Is it doable, yes. Is it ideal, not at all. It's hard to build stability and routine habits that are the basis of healthy living IMHO. Unless you are incredibly disciplined.

That being said you can try it for a short time as it's definitely sustainable for a year and if you hate it just move to NYC. That's what I ended up doing as I was in the same position.