Snails (guess I should say most) are extremely hardy when it comes to nitrogen posioning. When I say extremely hardy, I really do mean extremely.
Ammonia usually kills fish by damaging their gill tissue, making their gills not function sufficiently to keep them alive.
Even with long enough exposure to low levels of ammonia will damage enough gill tissue that the fish can no longer sustain.
I haven't studied exactly how ammonia effects snails, so I can't give a 100% certain answer, but I do know a little about snails and have drawn some theories how they can survive such conditions.
The snails I have seen survive very high ammonia levels and even extremely low oxygen levels (stagnant water), were ramshorn, pond snails and bladder snails (yes both pond and bladder species). I haven't seen whether or not other snails could survive the same conditions.
The snails that came on/with your plants are most likely ramshorn, MTS or pond/bladder snails.
I know most snails (ramshorn, pond, bladder, MTS, etc) breathe with "snail lungs" (pulmonata) and not gills.
Nerite snails (and a couple or so other snails I can't remember as well) though, do have gills they use to breathe though. And I haven't seen them tolerate high ammonia levels or not (they might, I don't know). If they don't tolerate high ammonia levels like snails with lungs, I would suspect the gills would be the vulnerable factor, such as in fish. And I would assume ammonia does not damage the snail's "lungs" or if it does, it takes . I do know very very high levels of ammonia can kill snails though. Again I do not know how ammonia kills snails exactly, maybe it's through damaging their gills/lung, or damages their skin, internals or what.
That's just my assumption at a possible explanation though. Snails might be more hardy to nitrogen poisoning for a completely different reason (maybe the snails have a special coating that protects them from the effects of ammonia). But however they do it, I do know at least Ram's horn, pond and bladder snails can survive very high ammonia levels and low oxygen levels (which is clearly explained by the "snail lung").
There are other possible methods for snails to escape ammonia poisoning though, such as burrowing into the substrate (MTS), climbing out of the water and/or respirating via surface air, huddling up in their shell (especially if they have a trap door), etc.
So yep, the snails can tolerate the tank cycling, as you can see it doesn't seem to be effecting them much at all (your level of ammonia is a whole lot lower than levels I've seen them survive in). Now fish are another story. It's a known fact of the damage nitrogen toxicity can have on fish. So again I would advise not adding fish until the fishless cycling really is complete even though the snails appear fine. You shouldn't have much longer to go as I see you have nitrites and nitrates registering. A finished cycle would convert ammonia into nitrite to nitrates within a reasonably timely manner. You want to keep the nitrogen at healthy levels for fish, which would be 0 ammonia, 0 nitrite and 20-40 or less ppm of nitrates.
Just to state, even though I acknowledge snails can tolerate high levels of ammonia, I still don't recommend subjecting any living thing to harsh conditions. For this case though, I know it was accidental and given the levels are low to snail tolerance levels, they would be alright. Water pH is a bit on the low side though, and I don't know if compromised shell health would change the tolerance of ammonia.
Nice puppy by the way. Pit? Haha, took me a little while to figure out what the pic was of.
EDIT: found some little articles on snail breathing
http://www.molluscs.at/gastropoda/index.html?/gastropoda/freshwater.html
http://www.molluscs.at/gastropoda/index.html?/gastropoda/freshwater2.html
