YES, YES, and YES....
I am terrible at keeping up with house type of chores and stuff when depressed. (probably when NOT depressed too, but not quite as bad...)

I think for me it is partly that when depressed I am triaging my life to get by. Just like paramedics do in the field, dealing with the most pressing concerns first (not breathing, gunshot wound) and leave the secondary injuries for last (broken bones, scrapes)....
So I do all of the things that absolutely HAVE to get done first, like going to work, paying bills.
And leave all that other stuff that SHOULD get done for later, like cleaning and laundry, if i have any energy left.

Also for me i think learned some bad coping behaviors, where i would let my place get absolute shxt while depressed and then take advantage of a mood up swing to clean the entire house and do all the chores i let go while down.

Plus, i have some issues with daily type tasks that you have to repeat over and over again. like mail. and cleaning. and dishes. etc.
its like it never stops. i am supposed to clean and straighten and do dishes et al and then DO IT ALL OVER AGAIN TOMORROW!!!

But. I have sort of accepted that i can be a slob. I don't encourage the unannounced drop in. So i try not to beat myself up for it too much. i think i assumed that negative critical self talk would somehow motivate me to actually do it. but all it does is result in a messy place AND feelings of crappy self worth. so while my way may be inefficient and i am sure if i didn't let it get so bad it wouldn't be so overwhelming, this is how I roll.
there are more important things in life than a spotless house anyhow...

but i can definitely relate.