As a customer of both, should I brace myself for untold riches post-acquisition, or………not? 
Don’t go shopping for that second yacht just yet.
I’d have gone for a Sunseeker myself, but as I’m a customer of neither institution it’s pedalo for me. R-
Newp. You are only a customer of The Co-operative Bank, you don’t have a share in it. The shareholders (the US hedge funds) will get a payout.
You are and will continue to be a member of Coventry BS, with a member share, but given they are buying and not selling, again - no payout. (And even if they did, if you joined after 1998, those shares would be automatically assigned to charity in the event of a sellout/demutualisation.)
You could always buy it on a Nationwide credit card and transfer the balance to the 28 month 0% Virgin one 
My Britannia BS membership was given away Co-op Bank for free - which helped kick off the downfall of the Bank so I feel Coventry BS should buy me a yacht or two.
I do also keep seeing references to Co-op Bank becoming a mutual again when it was never a mutual to begin with…
It wasn’t a mutual, but it was owned by one.
It still won’t be a mutual in and of itself when it’s taken over by Coventry BS either.
Given that the Britannia was what pulled the co-op down, you should have paid them
Hopefully, the Coventry and Nationwide have done proper due diligence this time on their respective purchases and aren’t similarly sunk.
That takes the Coop off the table as an option for me, I have had some poor personal experiences with the Coventry and don’t touch them as a result.