Wow, so I suck. This has been in my inbox for a long time and I either never got the notification, or I looked at it and thought I'd answer later and forgot.
But it's (over a year) later!!! So here we go.
The short answer is: it'd be messy as hell. I think she spends all of season one incensed that a guy she slept with as a one-time thing is following her around like a puppy, while Castle keeps trying (and failing) to convince her to engage in a repeat performance. Sorenson's appearance — and Beckett being completely enamored with him — is enough for Castle to get the message, and I think he chills out. But I also think they don't have a close enough relationship for him to poke at her mother's murder as early as he does in the show.
In my mind, he finds out the details when they get the Dick Coonan case. He's been shadowing her for long enough that there's a begrudging (on Beckett's part) partnership and a burgeoning friendship. Castle's like 30% in love with her already and doesn't hesitate to pay the fee for info on the killer, and he's there to prop her up and help her through it when it all goes to hell. So by the time the serial killer case arrives and Kate's apartment blows up, there's a legit friendship. Enough so that when she moves in with him, Castle gets that repeat performance and it stirs up his hope that there could be something more.
There isn't, of course. Demming appears and she latches onto him as a distraction from the awkwardness and regrets of letting her guard down with Castle. He goes to the Hamptons for the same reason and in the fall, he doesn't come back. He has no intention of coming back, and he's in and out of the precinct throughout his relationship with Gina. He does shadow Beckett sometimes, but mostly does book promo stuff and keeps his head down.
I don't think they grow closer as they do in season three. He's hurt, and she keeps him at arm's length, but they do have moments where the possibility of more is right there — in LA when Royce dies, after Jerry Tyson assaults Castle and Ryan — and when Beckett is shot, Castle thinks 'God, I could love you' but he doesn't say it. He dives in front of the bullet, and he begs her not to die, but there's no deathbed confession. When she shoves him away to recover he works the case with the boys but accepts that, once again, she's telling him she doesn't want or need him like he wants/needs her.
Coming back to the precinct, it's her olive branch that breaks the stalemate. Like Castle, there are feelings there, but not the depth that they are in the show. But she convinces him to come back and work full time, and that year is the one where they REALLY become friends and partners. Kate pieces her life back together, occasionally shares some of it with him after her therapy sessions, and when he asks her not to throw her life away -- she listens. She doesn't nearly fall off a roof, she goes to Alexis' graduation and holds Castle's hand while he cries at his daughter's speech. They have their movie marathon night and he invites her to the Hamptons for a week in July, which Kate accepts.
But there's still the deal that Castle cut with Smith after her shooting. Beckett is still digging into her mother's murder when she has time, but she's also spending time outside work in and out of Castle's loft, getting to know Martha and Alexis. They dance around the possibility of dating for a few months, but when Tyson tries to kill Castle they throw caution to the wind and just go for it. So when they stumble upon the info that helps them ID William Bracken (remember, no rooftop fight. No file recovery in this universe), Castle is forced to tell Beckett about the deal he cut for her safety. She's apocalyptic with rage, breaks up with him, and throws him out of her apartment and the precinct. She still confronts Bracken, but this time it is because she's been offered a job in D.C. and wants to do it without his shadow hanging over her.
A couple of years go by. Alexis takes a job at a nonprofit in D.C., and Castle bumps into Beckett at a random coffee shop. He's stopped writing Nikki Heat books, she's rising through the ranks in the AG office, and they talk. It's awkward. There's hurt and feelings on both sides, but they don't reconcile. He goes back to NYC. She goes back to work.
A few years later, William Bracken's presidential run ends when he's arrested by one of the most promising members of the Secret Service. Beckett isn't on Bracken's detail, but her security clearance and tenacity, as well as a ton of connections in law enforcement, have helped her build the case. She arrests him for her mother's murder and fends off offers from dozens of companies and agencies to take a job at the training academy.
A few weeks after the arrest, she gets a note in the mail. It's Castle, congratulating her on solving her mother's murder and saying he will be in D.C. for a book signing for his latest novel -- a political thriller. He invites her to dinner but understands if she doesn't want to see him.
She agonizes over what to do in the week that follows but, ultimately, Kate finds that the sting of betrayal has evaporated. When she thinks of Castle, it's mostly the months when he made her so happy. So she puts on her favorite dress, curls her hair, and meets him in front of the restaurant at 7:30 sharp.
And they talk for hours over delicious food, a bottle of wine, and cups of coffee. When the restaurant apologetically kicks them out, Castle offers to walk her back to her place and quips that it's not unlike the first time they had dinner together. But this time, Kate invites him inside. This time, it sticks. They get married a year or so later, two weeks before Kate's 40th birthday and four months before she's tapped to run for the US House of Representatives.
