If the show does well and gets excellent reviews, a Broadway run should occur in 2018.

http://www.theatermania.com/new-jersey-theater/news/paper-mill-season-half-time-the-honeymooners_80157.html

Why do I have the feeling that this won't do well?

For one thing, they did probably about 100 mini-musicals during the TV runs of the 50s and 60s, so a musical version is nothing new.

There is only 41 hour-long musicals in the 60's.
Nothing repeated or drawn from the 60's.
This will be very new.