From my experience YES YES YES desulfate those batteries!!!! We LOVE our battery minder desulfator. This is a personal testimony - I've brought back batteries that I thought were absolutely goners.
This is serious - my friend had a Nissan truck that was needing a visit to the scrapyard. It had holes in the pipes and was overall in bad shape but when the battery started getting weak and unreliable he decided to park it. This was in 1999. Well anyway, it never went to the scrapyard. It sat. And sat. AND SAT.
I was over there one day in 2014 with the family with some burgers on the grill and we got to talking in the backyard. He then said "I need to get rid of that truck". We went over to it and just kind of were kicking at it.
Anyway, we got to playing around with it. Of course the keys wouldn't start the truck at all.
So we pulled the battery. Opened the fill hole covers and looked inside. ALMOST dry. Goner....
Anyway, I told him about desulfation and how it seemed to keep my batteries going endlessly. So for kicks and giggles, we put some distilled in the fill holes and covered them.
Meter read .2 V (yes POINT 2)
DEAD!!!
Anyway, I put the battery minder (wall wart type) on the battery. It wouldn't even read the battery as a battery. I guess it needed a voltage to start "kicking in".
So we put a battery charger on the battery. Charged for the next hour. Then we pulled the charger off and ALMOST Immediately put a meter on the battery.
It started at 8V, 2 seconds later 7V, 2 seconds later 5V, then it a bit slower started ticking to 1V. DEAD. We did this several times in the next 15 minutes. Charger then watched the battery tick down.
So we put the charger on it again. With Meter it was reading 12V with charger! (It should read higher with the charger on). This battery was toast!
So anyway, we got this crazy idea. Let's keep the battery on the charger then extremely quickly remove the charger and put the battery minder on the battery.
Well we did it and the battery minder stayed ON! I suppose something residual kept the battery at an upper voltage momentarily to allow the battery minder desulfator to kick on!
Anyway, we grinned. We left it for fun.
A week later I returned and he had it still on the battery minder. We pulled the Battery minder clamps off and had a meter.
10.84V 2 seconds later 10.73V 20 seconds later 10.54V. After an hour 10.48V and it held!!!!
Back on the battery minder.
2 weeks later I was back. Battery was at 12.22V and held steady after 20 minutes at 12.10V!!!!
We put it in his old truck. Put on the leads back onto the batter. Went into the truck - grinned at each other.... Then we cranked..... CLICK CLICK CLICK. It was the solenoid!!! We died laughing. Seriously we could not believe it. It didn't have the crank power. Radio powered!
Back to the battery minder.
This time we left it for 1 month. (I guess our motivation increased)
The battery this time held at 12.68V after 20 minutes of being off the charger.
We stuck it back in the truck, connected the terminals.
Then we went to the moment of truth. Turned the key and the STARTER STARTED TO CRANK!!!! The engine did not start (no fuel) but the starter began to crank for sure!
We were amazed. Seriously amazed.
We put in some fresh fuel with some marvel mystery oil, put one drop of MMO in each spark plug hole, turned the key to ON, and heard the fuel pump start.... Sat there in anticipation for 20 seconds.
Turned the key, crank crank crank...... CHUG CHUG, START - Start - START!!! Engine STARTED!
Lots of smoke.... But it was running.
We were laughing... Just could not believe it.
Went out with alternator on the battery, read 13.84V.
Left it running for a while.
Turned it off.
The next day he went outside and it cranked again! Started again! (I wasn't there).
2 weeks later he had it sold to a junkyard for $150. He got better $ because it started. It was a piece of junk by then for sure... But that's not the point.
What I'm trying to get at is this battery by no means was suitable to rely on whatsoever. It was a fun experiment for us guys over beer and burgers. The battery "worked" though after all those years of sitting dead (which is terrible for batteries).
So what I suggest is if it can do that for this total landfill worthy battery, what it can do for a battery that is newer and just getting weaker is beyond me. I'm on year 8 with some of my batteries. Every 6 months I put them on the desulfator for a couple of days. Still going strong. Needless to say, I'm definitely in the "DO IT" camp.