I'd imagine it wont make or break either route but will help the viability. I believe that the connecting will do well because :
1). There was alot of transfer pax when BHX and MAN were connecting routes, and they have better routes to the US than Edinburgh
2). Looking now fares are very cheap.
I will take a random Wednesday in July. Lets say the 12th-19th July.
Aer Lingus
EDI-SNN-JFK £706.51
EDI-DUB-JFK £733.24
American Airlines
*EDI-JFK £998
British Airways
EDI-LHR-JFK (Return via LGW) £990.98
Delta
*EDI-JFK £993.54
EDI-AMS-JFK £962.84
KLM
EDI-AMS-JFK £966.04
Lufthansa
EDI-FRA-JFK £1000.77
United Airlines
*EDI-EWR £997.44
Based on 1 adult
So what's obvious from above is that Aer Lingus is miles cheaper than the rest, with a stop through Shannon being the cheapest method.