Oils come in a range of viscosities, from ash felt and maritime grease to diesel, kerosene and racing car brake fluid. most oils you might sensibly choose for such a system are indeed more viscous that water, which means a stronger pump as has been mentioned. Oils can eat away at seals and hoses, again mentioned, but the automotive scene meets these demands. There are hoses that will take oils, there are seals that will too, oil doesn't have as good thermal transfer properties as water, but it's not as corrosive. If oil leaks, you have a clean up issue and possibly a smell of hot oil, but if water leaks it can cause short circuits and bridge from power feeds to that nice stylish metal case.
Remember, the PSU is directly below the LCS, yes there's a metal sheet between them, but it's not sealed watertight, so water can get around it. And it does.
I don't doubt such a system could be made to work, but it's likely to me a far bigger job than swapping the old seals and hoses for newer/better ones.
Silicone rubber hoses might be nice, but they have issues with gripping inlets/outlets. It's worth some research on the net for the well known and understood ways around them, but understand that stronger clamps can crush lighter weight spigots if over tightened.
I've owned 6 or 7 European sports models and SUV's (and modified most of them in one way or another) with oil coolers (one had an oil cooler engine and another for the gearbox) some were a small radiator, looking like a smaller version of the water radiator (about the same kind of size as the LCS radiator), some were basically a pipe with wires on - to increase surface area. Aftermarket oil coolers can be found online, as can everything else you could need, it won't be cheap. You may find that a bit of creativity and some bits from the pick a part yard could give equivalent results for a fraction of the cost - take care with used parts they may be great or they may be trash, check them over carefully before handing over your cash,
buyer beware.
Its not corrosion per se, just residue that can harm things
There's deposits alright, but you can also get corrosion too. Deposits can usually be cleaned off, but you may find contacts and circuit board tracks damaged or eaten away completely in some (usually small) areas. These can often be repaired, but it's time consuming and potentially expensive.
I got a LCS from a dual processor G5 and examined it closely.
If there's damage to the CPU boards, check the PSU carefully too.