Is it safe to test a (possibly) salt-water damaged lens (Tokina 11-16mm) on a new camera body?

It could damage the new camera, but if everything is dry it's quite unlikely. But if you're risk-averse don't try it.

If there are or were any signs of salt water having got inside the optics it will be ruined optically anyway, so there's no point testing. Unless the lens is worth quite a bit it might be worth the test, but not if the camera is expensive.

I run canon kit and have a very old body that I would risk to test a lens. If you could pick up a compatible body second hand for much less than the cost of a new lens it might be worth it for testing. Even a body with a known but irrelevant fault could serve this purpose.

My experience with saltwater damage is from my family business in an electronics repair shop where we handled board-level repairs for major manufacturers (including Sony & Panasonic.) The consensus always was from us, the manufacturers, and independent insurers that once we confirm a device has had saltwater in it then it is immediately "beyond repair".

There are a few reasons... as a repairer you simply cannot guarantee that the device will work once it's had saltwater in it. The way salt affects corrosion means that if a device passes testing in the morning you does not guarantee that it still might in the afternoon. Repairers simply won't take the risk when the device might be back in their hands the vey next day.

Typically though you can wash it off, the true saltwater damage is rarely visible to the naked eye. Circuits are very fine so any corrosion issues don't need to be especially large (or even visible to the naked eye) to cause either a broken or short circuit may occur and there's no way for a repairer to spot it.

When you look at the potential damage that might come from the failure-mode of the lens it is the kind of damage that could take out your replacement body. If you can afford the risk that you have a ticking time-bomb on your hands that means you may have to replace the body (again) and the lens the very next time you use them (or it may be fine for years) then by all means go for it, but personally I'd chalk it up to experience and replace it now.

If you look at a pinout diagram of an a-mount lens, it shows that there are, among others, "focusing motor power" (so, a non-logic-level power bus), logic power, and logic pins that are (from camera body perspective) logic outputs. If any of these got shorted together, there would be at least a theoretical risk of camera body damage - shorting any power bus to an output, or an output to another output, is often considered the worst case scenario with logic circuitry (most power supply circuitry will have safeguards against power to ground shorts, but not necessarily power to output). A lifted ground could also, in theory, cause problems especially in a scenario with multiple power buses. Applying motor power to a logic input could also be troublesome, since it might get shorted onto logic power by ESD protection diodes.