That would depend on how long the current second iteration of Serpents have been active for, and when the events of "The Devil's Shadow" (extinction of Carnefice Family by Ombras) took place.
Cause iirc, while it's not specifically stated how long the current Serpents have been active for, it's been sort of implied (by other characters, like Giocabbe, Luca, Gracie etc) that they have been for quite a while, enough to make their fame be a legendary status (not sure they were actively during "The Big War" or not, but even so definitely a long time).
So "Serpent" joining DeLuca after Carnefice Family's demise I think it doesn't really fit well, because he only became "Serpent" after joining DeLucas (I mean can't be one of the Serpents when he's still affiliated with Carnefice Family, no matter how much friendly terms the Family is with DeLucas).
And also, such scenario would mean Carnefice Family met its demise a long time ago before "Serpent" even started to get known as one of 4 Serpents. That's a really long time for Eiza to be under the chains of Ombra Family (and also long time for her sister Fina to be captive).
The 2 girls going through hardships for long period like that, if that was the case, I must admit it would make me sad.
My theory is, if Dante = "Serpent", then when he was young he first began as a student under Efrem learning the mastery of stealth and assassination.
Wilfred found out about Dante, and being in feud with Efrem, tried to lure Efrem's student away from him but failed.
Dante studied under Efrem, and became a master in assassination arts but eventually had a falling out with Efrem and sometime later, ended up with DeLucas (for unknown reasons which will be revealed later).
He became infamous as "Serpent" of the new 4 Serpents.
But years later, him, Cordia and Wilfred were too late too stop the Family's demise with Efrem perishing in "The Devil's Shadow."
Eventually he is able to pay his debt to his former mentor by being the commander in charge of Ombra mission, and his able to save his mentor's daughter with MC's help.
Things may or may not play out like above, but that's my theory (with assumption that it hasn't been that long time since events of The Devil's Shadow till MC's Ombra mission).