Ok, I've seen that type of set up. (Ours was a winter cover but god knows wh anyone didn't put in on for a few years til fanny Mae took over!)
I'm a little concerned about the idea of turning on the equipment without removing at least enough of the grate structure to have access to the skimmer and main drain to try to clear around it even though you'd be working blind.
Our fear had been clogging the lines with debris and then having a second and more difficult problem.
I discussed your situation with my husband yesterday and asked him, knowing what we now know, he'd advise you to do. We pretty much agreed that if we were to do it over again, it would have been easier to use the sheet method with a trash pump to expedite getting a majority of crud off the bottom.
You'll still have to SLAM (shock and maintain) the mixture of new and old water and whatnot, but it would dramatically reduce labor and time span of recovery, we think. That way, the trash pump is getting the bottom crud out enough to safely run the filter, but the visqueen sheet would damp down the smell in the interim. Just a thought.
You have some time to decide before closing, so here's a thread you can read from the guy who tried it a few years ago.
http://www.troublefreepool.com/threads/52373-Foreclosure-Swamp-in-Pensacola-Florida!/page4
With all that said, enough chlorine and scooping will in fact do the job. Here's a pic of my swamp recovery across twelve days of shock and awe...you will note there is one image where you can see the water has become pretty clear but there's still a big pile of leaves in one corner that we'd missed....which is how I know that with enough chlorine, it will still clear even with some organic matter left behind
we hadn't wanted to vacuum blind, as we only had the vac that connected straight into the skimmer.
I'm posting this so you can see the color change progression. That is a big clue that its working