Can a regulator ever fail in such a way that it wont regulate the pressure at all and the output psi is the same as the input (850psi)?
Yes and this relates to what you might want to do with the regs which have been wet. Inside each reg is a diaphragm, made of various types of flexible things like rubber, plastic or combinations of things for a stretchy,flexible "wall" between the high pressure and a spring. Looking at the drawing, the high pressure presses down while the adjustment spring presses up to move a form of needle in and out of a hole to regulate the pressure.
The hazard of these getting wet, depends on how wet, how long and what the diaphragm is made of. Like any material, some fail sooner than others and get a hole in them.
But if they get a large enough hole and fail totally, the spring is then not pushing against the gas but the whole reg body is filled with gas as the needle valve is no longer part way down in the hole but pushed totally up and the hole is just open!
When this happens, the high pressure will usually break the weakest spot on the output side, often a tube on a diffuser or such. Then there will be lots of CO2 flowing until the tank runs dry. It is not a super big issue, but it can happen and will blow out a small item in the low presssure gauge called the bourdon tube as it is just a thin metal foil item.
But it is only a thing that might happen and something to know and be aware of when deciding. Many regs have been wet and do fine. Some will get weird if hard water deposits form in the area where the diaphragm needs to slide up and down. Where I found this was in telephone work where we had to put tanks and regs in manholes to try to keep cables dry. Sometimes it worked and sometimes we came back after flooding to find a mess! But those are pretty extreme situations. CO2 is not dangerous but it can make a mess if it stops working correctly.
A point on the valves pictured to keep in mind? Those are using a small/ tiny thread called a 10-32. Ten is a size of screw used in the US and 32 is the number of threads per inch. So that joint depends on a pretty thin portion the size of a screw to hold it up and does break pretty easy if we hit it.