Does it, and its elements, behave differently depending whether it fights a bunch of smaller templates assigned to various positions / designations, as opposed to a universal template like itself?
Ugh! That's far too broad a question -- with too many variables -- to give much of a coherent answer.
Yes, but no.
Bombardment fire by bombardment rules. AA by AA rules. Units in Front-Line Attack function by front-line attack rules, and front-line defense by FLD rules, etc.
Unit type (infantry, vehicle, static, etc.) affects max fortification (and therefore speed of fortification), evasion, breakthrough chance/ability, and some other stuff. Target Armour & HP ratings affect what happens when they're hit -- and that's on a per-element basis, since a 'unit' can include any mix of any types. Your six-shot HCAP can 'hit' two INF-PW, one INF-LOG, one MVH-AA, and one STO twice.
A unit can only be in one 'place' at a time -- 100% of that unit is in FLA, or FLD, or SUP or REAR -- and if you can mange to divide it between multiple areas then that's not ONE unit any more, it's two (or three, or four, or whatever).