The "Introduction" event in the beginning of the game when Luna gives MC a guide of the house actually tells the player following:
I highly doubt it.
In pretty much all mafia fiction breaking the Omerta or changing your loyalty (i.e. betraying/turning one's back on the Family) means pretty much a death sentence for that person.
Look at what happened to Trino. We don't know the full story behind his actions (even though he claims he did it for the money), but due to that betrayal he got the death sentence (though it was done unceremoniously in Cordia's office due to Antonio's short temper, it still would have happened in The Woods, regardless).
I'd imagine it's the same for every DeLuca-verse Mafia Family out there.
Omerta and the one's Family loyalty lasts for life; and looks to be an unbreakable bond.
Eiza (and probably rest of the few remaining Carnefice Family members) is an exception because her father (the Don) is dead, & Carnefice Family is pretty much extinct (i.e. no more), which makes her be available to be under Contract to DeLucas and be on MC's team.
But that is a very rare case.
With Fawkes, I'd say the only possibility for him to be officially in MC's team would be, either
- Fawkes' father somehow pledges loyalty to Cordia and willingly becomes a Sub-Family of DeLucas (not likely to happen since Feni Family is a member of Bonanzo Family).
or
- Feni Family somehow gets in an alliance with the DeLucas (also not likely, due to the same reason as above, since Bonanzo Family is in an antagonistic relationship with DeLucas).
both options which don't really have high chances of happening anytime soon.