In Firestone, it definitely wouldn’t be admissible in court. We don’t have any spontaneous declarations/utterances clause, so you can quite literally say anything while detained before your rights have been read to you and it can’t be held against you in court.
Do note that probable cause (what is necessary to arrest) is a LOT less of a burden than beyond a reasonable doubt (what is necessary to convict), however.
Now, as for in real life:
Danny is correct that a confession like this, though it would be admissible in real life, would likely not be enough to secure a conviction without supplementary evidence. If there is no body, murder weapon, or other form of physical evidence, then more often than not a confession alone will not result in a guilty verdict.
To answer your question:
I would say you can definitely consider arresting them at that point. They only need to be read their rights for that confession to be admissible in court – they can still have it used against them for an arrest without their rights being read.
For an arrest, it is fine.
For a conviction in a court of law, it is not.
District Court Justice