I anticipate that there will be 4 possible concurrent scenarios:
1) Assault on Logan Run
2) Charlie's Mercenary Mission #1
3) Escort Mission
4) Random Encounter Mission
Assuming that #3 is referencing the Ixian mission, Yuri will call the Queen again briefly prior to the departure of any units on #1 and confirm what the move value of the units in need of escort are. If they're moving at faster than infantry speed we'll want to avoid putting infantry in the escort group so as to not slow them down... which, unfortunately, nixes the possibility of Yuri leading the most diplomatically-related of the missions and takes up some of our scant cavalry assets. On the other hand, if they have infantry in their group then he might as well lead our party there, and we'll be able to send more troops more easily.
Given that turns are fairly sizable and he has little else to do with his move (thinkagrams don't exactly eat entire days), Yuri is inclined to lead short-range foraging groups in an effort to be productive. He probably won't turn up much given the limitations of Move, but he can cover hexes that the other foragers aren't hitting and even a handful of shmuckers are better for the side than the zero he gets from sitting in Dis City drilling at weapons and toying with the female units. Any units who aren't doing anything particularly productive already and have a foraging bonus but could use some leadership can come along; I'm not sure how much leadership helps with foraging but it shouldn't hurt.
It is likely that Yuri will call the Breatheairians at least once during either Turn 11 or Turn 12, but he'll confer with Tod beforehand- what exactly is our overall strategy and timing, and given that, what impression do we want to try and give the elves? The biggest reason to call them- aside from seeing the funny looks on their faces- is to give them misinformation and probe them for anything they might let slip, but ultimately that's done in support of our military strategy, so having specific defined military objectives would help out a bit there.