ATP and type ride
Yessir, you can take your type in the Citation and get your ATP at the same time. The PTS are one and the same for both. Lots of people do it that way.
Just off the top of my head, I'm sure FSI can type you in the Citation. Undoubtedly there are other providers and other posters will have suggestions.
Do I understand that you'd have to fork up the $2K for the ATP and type? I'd think about that carefully. You can always get your ATP in a light twin at your local airport or a place like Sheble, or get a single-engine ATP in a 172 to keep your written from expiring. Sure would be nice if you could get your ATP and be typed on the boss' nickel.