Hypothetical questions get hypothetical answers.
Generally speaking, if the subject was not being interrogated while in custody, the statements probably are admissable. I think that it goes without saying that details matter. Many disputes about suppression of such statements likely revolve around this very issue of whether someone was or was not in custody at the time the statements were made..
On TV, police always read Miranda rights immediately after arresting someone. That's TV law. A Miranda warning generaly is required if someone is in custody AND the police want to interrogate him or her. So, if the police were summonded and someone voluntarily made incriminating statements before actually being in custody, those statements could well be admissable.
It also is well to know that the remedy is simply suppression of the evidence, in this case the statements. If the DA has other evidence, it can go forward with the case.