Assume a formation which hasn't activated in the current turn has lost some units which brings units in the formation out of formation coherency.
Can this formation carry out an action with no moving part (eg Overwatch, Sustain, Marshall with shooting, etc) and still not loose any units die to out-of-formation issues?

After all the rulebook says the following:

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Answered here:

1.2.1 Formations
Every unit in a formation must be no further than 5cm from at
least one other unit in the same formation. In addition, all units
must form a ‘chain’ without any gaps of more than 5cm.
Sometimes the units in a formation will become separated due
to enemy fire or assault. When this happens, the formation
must close back up again into a legal formation when it next
takes an action (see 1.6.1)