Not really. It takes 2 years to meet citizenship criteria and until then you are illegal without a visa but it's unenforced at ground level and not even a crime. It's actually much easier for many to obtain citizenship by residing illegally without permission and then applying under constitutional provision which doesnt care their residency was illegal.
That is the method to obtain citizenship for most without means is you must act without permission and then run down the clock.
It sounds like they do have permission, it's just not "official". If the law isn't enforced at all, and breaking it isn't considered a crime and there's no punishment for simply ignoring it, that sounds like tacit approval to me.
That's one way you could interpret it. You might say the same thing applies to visa overstays in the US, which isn't a crime and essentially unenforced except at easily predictable attempts to elicit self snitching at inland border checkpoints.
Huh? Overstaying a visa in the US isn't a crime AFAIK, but they can still detain you and deport you if you're caught. "Not a crime" just means they won't sentence you to prison for an offense, just like many other offenses are not crimes, but instead are torts or violations (like parking tickets): those things are still enforced, and you will (or may) suffer some punishment for them. When you said that Argentina doesn't enforce its law, I took you at your word, that it literally doesn't enforce the law at all.
The US immigration authorities do occasionally do raids on employers that are known to employ lots of illegal immigrants (which can be people who simply walked over the border, or people who overstayed a visa). It's not unenforced. For people in higher socioeconomic strata that blend into the population better, it's not that well enforced probably because it's just hard to find them, and local law enforcement doesn't deal with it.
I knew you'd understand these nuances a lot faster once presented with an American imperfect analogue. The truth as I gather is somewhere in between -- deportation extremely rare but possible especially in case of serious crime.
That is the method to obtain citizenship for most without means is you must act without permission and then run down the clock.