Yes, Ready Status not being ready will show up as a failure for DMV emissions... in my state at least and many others that I know of so I suspect NY is same.
Purpose is to ensure the emissions system is functioning correctly... otherwise one could just clear codes and/or CEL right before testing and subsequently pass before failure is noted again by sensors and DME.
The Ready Status will change after some regular driving... can't recall exactly the time/distance parameters. Otherwise, somewhere in the archives here there is a specific driving procedure (something like 35MPH constant for X blah blah blah...) to get it to change to ready quickly.
Good luck and glad you're making good progress
