Possible. Although I personally think that would have been mentioned. But maybe not.
If it was "body parts," they would have no way of knowing immediately if all the parts were there. It was a body intact enough to sex it.
I am envisioning a regular old chest freezer, like the ones we have. Not anything capable of "flash freezing" as one would find on a fishing vessel. Flash freezing capability, even in the best of freezers (upright ones are better at this) is still not all that flash.
But, the state of decay (when put into the freezer) would be testable, yes. If there was a delay in getting it to the freezer, absolutely forensic testing can tell that. This is something you can do at home with a roast, if you wanted to. If you leave it until it starts to decay and then freeze it, you can still smell the decay - which is coming from biochemicals - and those are testable, even before a complete defrost.
I don't consider these discussions "ghoulish," of course. For all we know, it was body parts (and LE is suppressing that information).
It would make a difference in which crimes the culprit is charged with. They probably want him/her to come in quietly and they probably have a good idea who did it.
LE has clearly said that there are no immediate signs of traumatic injury (being dismembered would be high on the list of traumatic injury - and no way of telling immediately if it happened pre- or post-mortem - we've looked at a couple of cases here on WS in the past year in which someone attacked someone else with a chainsaw or reciprocating saw).
I'm going with "person died and was put into the freezer." Our larger chest freezer is completely capable of holding the body of most average sized women (and larger). Or an average sized man, for that matter - but would be hard to put someone over 6 feet into it, unless they were really skinny.
I envision a scenario in which a relative was living in the house as a kind of caretaker. Person died, they freaked out and used the freezer, then ran off somewhere. The fear of being questioned by police may have been present. They'll figure out who she is and get her medical records, that will help. And if she's been frozen since near her moment of death, they can find lots of things to study inside her body to try and figure out CoD.
She didn't put herself in the freezer! (Or at least, that's very unlikely - I suppose someone could suicide in this manner, but...that would be the first time I've heard of such a thing!)