Yes. It would be a good idea to remove the sediment if it can be done without damaging the battery.
I wondered about a long thin tube with a tapered tip which could be pushed through the plates somewhere.
I think this might work but it would only be good for the lighter particles and would likely get blocked easily if larger shards of plate are shed.
Making holes in battery cases is not a good idea in my book. Apart from the potential mess to clear up, repairing the holes, though not at all impossible, is a chore. - but this is probably the best way to clear a shorted cell which is that way due to conductive sediment building up at the bottom.
The small 12 V pumps in electric kettles here use magnets to spin the pump that pours the water out of the 'spout' at the top. And the impeller is encased in plastic, as is the rest of the pump which is in contact with the liguid. So there would be no corrosion to worry about.
The problem would be to make it so it could be applied and later disconnected with a minimum of spillage and hassle.
The pumps I'm thinking of are not self-priming so they must be located lower than the electrolyte or at least momentarily below the liquid until there is sufficient pressure to continue at a higher level.
I suppose a raised portion of a bench would do the trick. And perhaps have a guide behind it so the battery could be tilted sufficiently to enable welding or otherwise sealing the hole.
Hmmm! Six cells and six holes.

Are there plastic screws which can be used to fill the void? Yes, I suppose so. But will they be reliable and not leak? Maybe if they can be welded, but a solvent would be better.
I'd love to make that sediment-filter, but it'll have to wait a bit.
These days I'm selling an average of one battery a day. My charges are cheap mostly because I'm still incredulous what I'm doing actually works. But I'm becoming more encouraged as time goes on and have already started to charge the price I wrote on my brochure rather than grant discounts for no good reason.
I usually set a three day limit on desulphating. In most situations if the battery isn't coming good after a couple of days it has other problems, and as this is dumped-battery-heaven I can be a bit 'picky.'
But I've got two 150 A/h marine batts being done in parallel and they've been pulsing for about six days now. They are huge, so I've coupled a hefty pulser along with a regular charger to get the job done as quickly as possible. The cells in those had E which registered in the upper RED zone of the meter. Four cells are inside the green, and all the rest are at the green/yellow border with only two cells actually inside the yellow zone. I can estimate they'll all be good in two days. I'll be glad to get them out of the way as I want to get more of the little ones done as they are popular.
Someone at the used car shop has asked if I can do a m/cycle batt. I said I'd try. I picked it up and on testing it was 11.24 V. But it doesn't seem to be shorted - yet.

The float in the meter didn't rise from the bottom of the tester on any of the cells.
It's about 16/18 A/h. A 'maintenance-free' job, and the plates were all fluffy and white.
I used a fine-nosed pair of pliers and yanked-out the plastic inserts in the 'wells' which were exposed after I prised the cap off.
The cells are all approaching the yellow mark now, and I think by tomorrow all the cells will be in the yellow zone and will be nearing the green.
Things are looking up. But I'm still not sufficiently confident to scream for business from the rooftops.
And thanks for the new links SeaMonkey. Actually I'd read those too!
* New pulser in the planning stages.

What has been won by the brave at great cost can be lost cheaply by fools and once gone can rarely be regained and only then at great cost.