Sure, its possible that They may have done something but also remember that Gambino was responsible for Genovese going to prison. So its also possible he would've have been fine with the move, if it were to really take place.
Gambino was in no way responsible for Genovese going to prison. If Vito had any inkling at all that he was set up anyone and everyone involved would have been hit like Costello, Anastasia and Moretti were.
The word on the streets is Costello, Lucchesse, Gambino conspired to get Genovese in prison. Whether its true or not, doesn't matter because Genovese was removed from the situation. And by this time Genovese's "supposed Loyalist" like Tony Bender Strollo felt it more lucrative to go into business for himself. This is also the beginning of the whole "sleeper" powers truthfully running the Family in the shadows. There was so many powerhouses in that Family, I'm sure they (alot) were glad to see Vito go. Nobody wants to deal with a tyrant after have years of relative peaceful prosperity under Costello.
"Joe Bananas went after Carlo Gambino, the war went on for seven years..... When guys go to the mattresses, they're not out earning" -Tony Soprano
