My bike has a square taper 68mm width cup and cone bottom bracket that is wearing out. I was hoping to replace it with a sealed cartridge (shimano UN55 or similar) but then I found that the spindle length isn't the same on each side - the right spindle end is 4mm or so further from the centre than the left. I think that modern cartridges are symmetrical, so the two ends are the same distance from the centre. Is it possible to mount a 68mm symmetrical cartridge slightly off-centre using a spacer? If I put a 2mm spacer on the drive side then the new (symmetrical) cartridge would be the same as the old (asymmetrical) cup and cone. But I'm a bit worried that a) there wouldn't be enough screw threads engaged on the drive side or b) the non-drive cup won't screw far enough into the frame to hold the cartridge steady. Has anyone tried this? Does it work?
In principle it is doable. Normally sealed BB have 15 to 20 mm of thread at each side, so 4 millimetres of spacer wont make trouble regarding how deep the shell will thread in.
Regarding symmetry, it is even a possibility that you don't really need to install the spacer, because what defines this is the chainline, that is, on a single speed bike, the front chainring should align perfectly with the rear sprocket. On a triple chainring setup with multiple gears in the rear, the thing gets a bit more fuzzy, but (I) roughly watch for the middle chainring being aligned with the centre-most sprocket. I mention this because some cup and cone systems have huge tolerance and can be off axis without any apparent trouble, and in your case, it is a possibility that the spindle is just 2mm off to one side.
The second factor is whether the cranks rub or collide with the chainstays. Both arms should pass by at roughly the same distance from the chainstays.
So, before deciding whether you need a spacer (and if you haven't disassembled the bike yet) check the chainline and the distance from the cranks to the chainstays, and see if you can detect any misalignment there.
Consider that there are some BB units that don't have a "lip" un the threaded side and therefore a spacer is not actually needed, they are locked in place just by the pressure from the locking cup on the other side, this type of BB can be set off to a side without a spacer (there is actually no way of installing a spacer). Other BBs actually have this lip to hold certain type of front derrailleur in place. In this case the spacer is optional, it is used just to fill up the space left by the absence of the derrailleur's mount ring.
The definitive yes/no compatibility issue is whether the theading on the bb shell is the same. Most sealed BB units I've seen have normal right hand threading on one side and left hand threading on the other. As long as your current cup and cone system is the same in this regard, you should be able to do the upgrade.
One final factor that may come in is the taper on the spindle. If by any chance the one you have is thinner or thicker than the replacement sealed unit, the crankset may "sink" in deeper or not deep enough.
Since you are going to do an upgrade, not a direct replacement, I advise to take the bike to a shop and compare (using a caliper if possible) your actual spindle to the one on the sealed unit you plan to install, just to be sure.
Phil Wood make a sealed cartridge BB that can be shuffled 3~4mm off centre in either direction. I use one myself; the thread engagement is pretty solid.
I see no reason why your spacer idea would be any different, in terms of reliability - try it! As long as you have at least 5 mm of threads fully engaged, and the BB and adjustable "cup" are torqued up against one another nice and tight, it should be OK. But if it's a frame you care about, I'd pony up for the Phil... at least then any thread damage to the BB shell would be a warranty issue, as long as you could demonstrate that you'd installed it in accordance with their guidelines.
Different threadings, tapers and spindle lengths are available; make sure you pick the right one if you decide to buy!
You'll also need to buy the tools to fit it (it's non-standard). The cups are stainless steel, so you'll need to use thread lock instead of grease when installing. Pricey but highly recommended.