There is really no clear teaching in Scripture about how tidy the inside of our houses should be; so I can only give my personal opinion.
The only thing I could find right offhand that seems even remotely related would be Leviticus 15, which deals exclusively with bodily discharges and the purification of everyday items that might come into contact with that discharge. Bodily discharges related to a disease required a sin offering and a burnt offering. Normal, healthy bodily discharges (semen from men in verses 16-18; normal menstruation for women in verses 19-24) simply required a washing with water and no offerings.
Hoarding seems to be a completely different issue from cleanliness, however. I do agree that it is closer to a mental illness, but that wouldn't necessarily disqualify it from the sin category. At worst it could be an extreme form of materialism, which would classify it as idolatry.
But I would also distinguish between a hoarder and a packrat. People who are packrats are usually conditioned into that lifestyle as a result of growing up in poverty. I know that some people who lived through the Great Depression learned how to be packrats as a matter of survival. My grandparents were like that and they passed it on to my parents, who passed it on to me. As a result, I have a very hard time throwing some things away, especially if I can conceive of some way that it might be useful in the future.
I also think that obsessive cleanliness might be just as much of a mental illness as hoarding. GOD created our immune system and it works really well, so a little dirt and some germs are not going to hurt anyone (who doesn't have some kind of immune system disorder).