JSquared2 said: "Possibly -- but not necessarily. Recent examples likeWaverly Gallery, This is Our YouthandWiTwere all considered revivals -- even though they were making their Broadway debuts (and would not be considered "classics"."
Waverly Gallery premiered Off-Broadway in 2000, after a 1999 run at Williamstown. It opened on Broadway in 2018, so nearly 20 years after its original production.
This Is Our Youth was similar, originally opening Off-Broadway in 1996 and not opening on Broadway until 2014.
Wit premiered at South Coast Rep in 1995, opened Off-Broadway in 1998, and didn’t premiere on Broadway until 2012.
All of these had stagings at major companies in between, as well as Wit receiving a television adaptation. While Between Riverside and Crazy has also received some stagings with regional companies, at only 8 years between its original production and the opening of its Broadway production, it just, to me, feels a little more appropriate calling it a new play, in terms of awards, than the other three you mentioned.