Considering all the fantastic possibilities demonstrated by Ardent's ability I'd find it hard to believe that the Praeses couldn't monitor its use. They probably know that he turned an ancient space fighter into a teleporting bubble ship and can shut it down at any time it becomes a problem for them. It's still unclear as to what their scheme is, but most likely they wanted to get those that would oppose their invasion of Earth out of the way. Pate may be an exception. If he's smart he'll accept their offer to be an exalted middle man since I doubt he's going to get anything better. Given his expression I think he's so in awe of what he sees he might just forget to throw his weight around and readily agree without the Praeses providing a demonstration that would probably be aimed at Church.
Why would they offer Pate anything? His only leverage is Church, and it's not clear how much that means in this context. I could see them pushing Church out into space to flail aimlessly as he floats in orbit. At which point Pate is all alone up against a pair of pissed-off immortals whose friend he had murdered.
I'm guessing the whole point of Operation Blue Boy was to collect Alice and bring her up to the orbitals. Maybe Sedna too, but it's hard to see how they could have foreseen that. Pate is probably just an extra baseline human they have no use for. Church might be a bit of a bonus, provided they don't end up having to space him.
The Praeses plan will go more smoothly if its being carried out by a human most people know. And if there are unexpected difficulties Pate can be the scapegoat too. I think the scheme was to collect Alice and Church, however, Sedna is just a bonus. She could be a problem, but since she largely kept to her self by the time she realized what was up it would probably be too late to do anything. Alice told Gavia that if her people invaded she'd see to it that the losses would be catastrophic so she's fairly confident that she could defeat an invasion force and it's safe to say Church would have no problems, but that was when they were on Earth. Now they're in space and there could be plenty of countermeasures to neutralize the immortals which leaves Earth virtually defenseless. However, it Pate controls Church and he's willing to be their viceroy then they'll probably let him return since he would expedite their conquest immensely.
Of course if Pate does turn on the Praeses I could see things going down a little something like this: