It’s not in my use-vocabulary, but I’ve heard it (or more likely read it) and knew what it meant after a moment of thought. (North east, where we get lots of rain and not a lot of flash floods.)
Same here.
But how many know what a “cloudburst” is?
A local TV weatherman used to use “Gully Washer” when predicting heavy rain. Along with “Picnic Pounder” and a few others I can’t recall now.
Same as a toad-soaker, right?
Or a frog strangler. (though both of these sound more like descriptions of sexual deviants.)
Of course I’ve heard it. I would have assumed it would be known to all Americans of middle age or greater.
But such expressions don’t seem to be trickling down to the younger generations any more.
A gully washer is worse than a toad strangler. Except for where it isn’t as bad as a toad strangler. A toad strangler is roughly equivalent of a goose drownder.
In the dialect of the region where it is used, is it proper to use the word as it is misspelled? 
Well, sure. I used that term just last summer to describe a particularly heavy rainstorm we were having.
OTOH, ‘toad strangler’ and the other animal-referencing terms for heavy rains mentioned here are unfamiliar to me.
Is it a kind of bird? Or a Dickensian term for a slovenly woman?
It isn’t misspelled. (Slightly different suffix, but still relevant.) The “drownder” version seems to be used mostly for animal-weather relationships, though. (But what other contexts could you mention it in? A serial killer who uses drownding as his method?)
There is an episode of Maverick titled The Goose Drownder (but incorrectly spelled in the Daily Motion description.)
(I had never heard the animal-related terms before this spate of googling, either.)
All of these are lighter than a log-lifter.
It’s another term for “frog strangler”.
I think I’ve heard of a “chicken choker”–is that the same thing?
Only a gully nut could come up with a definition like that.
There’s a ride at Six Flags in San Antonio called the Gully Washer that takes you on a whitewater adventure through Crackaxle Canyon. Yee-haw!
I’ve heard it in Virginia, as well as “raining cats and dogs” and “frog strangler.”
After driving through a downpour I will tell my wife, when I get home, that our gullies have been washed. 
I (born 1984, southern Illinois) know what both gully washer and toad strangler are, and one of those days I might use one of those expressions, but I generally don’t; my dad (born 1953, Chicago) likes to use toad strangler.
I’ve never heard of goose drownder.