Ferdinand: No. Edelgard strips his family of power and as a result, his father is boned. Really. Boned. Even though Ferdie himself is a bit naive to inner political matters, this would cross a line and he would want to see her defeated.
Dorothea: Debatable, considering despite her hatred for the nobility, war is not something shes ok with. But its more likely she would stick with Edelgard.
Petra: Lmao no. She is not an idiot, and knows damn well shes nothing more than a hostage. Edelgard's defeat would mean Brigid independence and safety. The only way she would side with the Empire is to make sure Brigid isnt invaded again.
Linhardt: This guy wants to be a crest scholar. Its his ambition next to sleeping. Edelgard wants to crush that system. I cant see Linhardt being totally ok with that.
Bernadetta: No. She doesn't really have any real loyalty to her father and house. She'd want to join Byleth regardless.
Caspar: Yeah he would stay. He is very proud of being of house Bergleiz. He would believe Edelgard's cause is right and just.
Hubert: Serves Edelgard without question.
Felix: lol no. He may have beefs with Dimitri and his own dad, but those are more personal than political. He finds Edelgard's justifications rather foul.
Ingrid: Nope. Her country and the future of her house mean a lot to her.
Sylvain: Despite his hatred of the system, i find it unlikely that he'd betray his best friends in the whole world.
Ashe: I feel like he would join Claude, simply to find out why Lonato was a patsy. Maybe he wouldnt side with the church right away, but the Empire? Nah.
Annette: Hard no. She loves her country, begs for her father to return to her life, and would find Edelgard's cause repugnant.
Mercedes: Very no. She's extremely pious and the Empire's use of the Death Knight really upsets her.
Hilda: Nope. She's actually quite loyal to her brother, Claude, and the whole Alliance.
Marianne: No. She may resent her crest, but shes a firm believer of the Church of Seiros. She even questions if turning on the church is even forgivable if you poach her in BE.
Lysithea: Maybe, only to smash the crest system She and Edelgard both had been experimented on, so she may find common ground there. But since Edelgard works with the Agarthans, im not too sure Lysithea would be kosher with that.
Ignatz: While he isnt noble, he would not see the point of what the Empire is trying to do plus, he is a believer in the church
Raphael: He already lost his parents, hes not about to turn his back on his little sis so no.
Lorenz: He goes where Glouster is concerned. If his father sides with the Empire, so will he.
Leonie: Devoted to Jeralt as she is, she would blame Edelgard for everything that happened to him.
Church of Seiros:
Cyril: Hes literally Rhea's Pomeranian
Catherine: is literally Rhea's doberman
Shamir: She'd join the Empire if the price was right
Gilbert: Hes actually loyal to the Kingdom so no hell, he wont even join you on church route.
Hanneman: I find it difficult that a crest scholar would be down with destroying crests. He does have some fondness for the Empire as his former home, however.....
Manuela: Maybe, simply to ensure the safety of her opera squad.
Seteth: He would never turn his back on his family. He clings tenaciously to what he has left.
Flayn: Also would not betray her family. She bolts in BE anyway.
I honestly feel that a lot of moral mental gymnastics need to be done in order to justify siding with Edelgard for a huge amount of characters.