I don't believe that the JR East pass is more convenient in that situation compared to buying a cash Suica card. The Suica card can be used in all the turnstiles without ever having to wait in line, while to use the pass, you have to go to a manned gate which doesn't exist at all entrances.

The time spent to get the actual JR pass at Narita would be as long as buying a round trip N'Ex ticket, probably longer. It's easy to buy a round trip N'Ex ticket at the ticket window (just write the desired return down on a piece of paper) plus you even get a tiny discount (5%) for doing so.