Yes. He actually started the project. I believe the first gig was in support an LA animal shelter. Which one would think a certain person we know could get behind in spirit. Right now, they are doing it for fun but hinted at working on an album of originals.
Constant? He
rarely posts on FB these day and most times his posts concern either his (very charming) family or his songwriting work. I think the last time he
posted something Morrissey-related - not
replied to a friend comment, note the distinction - was for the 20th anniversary of
Southpaw Grammar in August 2015. And he was quite rightly proud of it and respectful to Morrissey.
Be careful with this generalization. Some of us had caught a whiff of "bullshit" about the personnel change very early on in Jesse's tenure - and were noting his deficiencies from the first American tour. And the people who vocally criticized Alain in those days mostly did so on the basis of his unpardonable sin of not being Johnny Marr.
(And, yes, Jesse's unpardonable sin is that he is not Alain Whyte...
The rhythm of life goes round, etc.)