Maybe as tourist but not 5* business
I was looking for an alternative to the NY Palace which is getting a bit dated and the website of The Alex looked nice and the location central. I might consider returning on a private trip with a budget but certainly not on my next business trip.
My room had a "corner window" which was half covered by curtains which could not be moved, so it was very dark (I was told I already had an upgrade from our corporate rate). There isn't a proper lobby area, it feels like a company's corporate reception. I also did not feel the front office staff was particularly welcoming. I arrived at around noon and there were several uncollected room service trays sitting in the hallway. No free Wi-Fi anywhere in the hotel. The public hallways are soulless. I had trouble with phones, my boss' TV did not work. My safe was locked, the instructions about the default code had gone missing. 
I had to laugh reading about one reviewer mentioning the flat screen TV in the bathroom as amenity - the bathroom is so small I kept hitting my elbow and I was never quite sure from which position I was meant to watch - the loo?
The positives - it was generally clean, very convenient location to Grand Central and the bed was very comfortable. I did not experience the luggage outsourcing one of the other reviewers commented.