Yes, any good detergent oil (and "normal" oils today are all detergent oils) might eat away the crud that is masking leaking gaskets and seals in any old engine. And synthetic oil even more so, because it is simply more slippery than dino oil.
But this isn't the sixties, and oils have come a long way. If Volvo says "Use SAE10...use SAE20...you have to ask yourself what does that mean. The SAE numbers just mean how thick the oil is, and how long it will take--literally--to pour through a SAE standard test funnel. THAT'S ALL. It means nothing about lubrication properties, just "how thick is this goop?"
At low temperatures you want SAE10 or less because it will allow the camshaft to rotate sooner. When a cold engine starts, and there is no oil film built up around the shaft, the shaft literally slams from side to side (like a bowling ball in a clothes drier) in the bearings and they chew each other up.
Synthetic oils generally have better "thin film lubrication" properties than dino oil, meaning that even though there is only a thin film of yesterday's oil on the bearings, it still lubricates better than dino oil would. And in fact, the oil film can "get hard" when it is slammed, so it isn't displaced during startup as easily.
So they are saying, you need 10W oil or a lower rating in order for it to be thin enough to allow start-up lubrication in the cold. Today you can get 5W and even 0W rated oils for the same price as 15W50, and get even better protection during startups with no drawback. Thirty years ago, the drawback was that the additives and the sino oil broke down way faster when they pushed the specs that far, so the old oils wre not reliable or durable.
The new oils are.
The other side of the spec they are giving you is the 20-weight oil for normal temperature operation. That's pretty thin for a modern engine, it won't give much protection at high temps or speeds, but let's assume they want it for a reason. That would mean a 0W20 or 5W20 or 10W20 oil would be perfect for you, but I don't think you'll find it. Modern oils usually run to a #W-30 rating as the lowest.
What would that do to your engine? Well, again, a modern 30 will lubricate better than an old 20 would. It will be a little thicker, so if your engine has tight tolerances it might steal a little more power at speed. It might also need an oil pressure (pump) adjustment if it turned out the thicker oil pumped through slower. But given the way these are usually not critical parameters, and the other lube properties of modern oil...I think I'd trust it.
Of course you can always call a couple of pros, Shell, Mobil, Castrol, QuakerPenn, all have toll-free tech support and they will not tell you to put something wrong in your engine, because they generally warranty the engine against oil failure when you are using the product they recommend in it!
Obviously you need a diesel-rated oil, not a "spark" oil. Make sure to remind them of that. But I'll bet there are at least a half dozen suitable products out there, and unless your gaskets and seals are just waiting to fail anyway, synthetic oil shouldn't hurt them. If the makers say not to use them, that's something else again.
But Volvo? These days, who is Volvo? Ford? Tata Motors? An engineer, or a guy reading from a Customer Service Script Binder?
Check for the API and SAE web sites, and their explanation of just what their ratings do and don't mean. I think you'll find a huge fog (and burden) get lifted, and they do it very quickly.