I think 4th ID or 9th ID in Vietnam was built as a cohorted unit from the ground up -- draftees from day one grouped, trained, sent to Vietnam together on that division's deployment there. Apparently worked well, but they subsequently turned into the usual individual replacement format after the first year.
Anyway, in a T2K sense -- cohorts coming out of training units would be broken up, but an effort might be made to front load people from the same training cycles to the same units needing BCPs.
Sending the drill sergeants off with them wouldn't probably be done. The military has tried pretty vigorously to build a robust and redundant training cadre capability and shafted lots of guys with drill sergeant duty who're only there because their career demands it. Still, even with that there's going to be heavy attrition among qualifed Drills and most likely the preferred course of action at the big picture level would be to keep guys in those positions until such a time as the need for mid level NCO casualty replacements (and mobilization of the USAR drill sergeant units) pulled them out of the mix as a last resort.
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