Not a lawyer nor intimately familiar with the subject, so until someone more knowledgeable chimes in and at risk of making a fool of myself:

I believe it depends on context. If you're in police custody and being questioned, you need to be read your Miranda rights. If the police show up to your door and you suddenly blurt out a confession, I don't think it matters.

That's mostly correct, but it gets even more contextual: if you confess right when you greet the police, your confession is admissible.

However, once the police start asking questions, they have to show they had not created a "custodial" situation in which the suspect was not free to leave (or in this case, to close the door and tell the police to fuck off). In most states, the burden is on the defendant to show that a custodial situation was created; in some states, that is presumed and the police have to show that a custodial situation was not created.

You do have to be Mirandized if the prosecution expects to use that confession--or any evidence derived from that confession (under the fruit of the poisonous tree doctrine)-in court.

For the record--I am former public defender. And I successfully used the failure to properly Mirandize a client successfully many times to block the prosecution from introducing evidence.

I think you would to use that in court - https://en.wikipedia.org/wiki/Miranda_v._Arizona - IANAL.