Okay, so it is possible to generate wallets in an offline mode without ANY connectivity using bitaddress
Correct.
But how does the system (the blockchain) knows then that this address exists and you can send BTC to that address?
The blockchain is just data. It does not know anything. It does not need to know anything.
You are now asking questions that require an understanding of the technical details of how bitcoin works. "Addresses" don't actually exist at the technical level. Neither does anything that could be called a "bitcoin". Those are just abstract concepts that we humans use to make it easier to talk about transferring control over value.
Imagine for a moment that I write a note that says that I want to transfer control of my pencil to someone named "John Smith" who lives at the address of "123 Main St." with an ID number of "1S3FH45692".
How does the paper know that this person exists and that I can transfer my pencil to him?
The paper doesn't care.
Now imagine that somehow this note on paper could be made into a binding agreement that I could not change. If the person actually exists, then they could claim the pencil. If they do not exist, then the pencil would be stuck unclaimed by anybody forever (or at least until that person eventually exists).
Bitcoin operates in a similar manner.
When I send a bitcoin transaction, the transaction has a section of data called the "output". The output is assigned a value, and then is encumbered with a requirement that someone must meet if they want to be able to spend that output. The blockchain doesn't care if that requirement can be met or not. It simply records the fact that the requirement exists.
Then wallet software converts that requirement into a string of letters and numbers that we humans call an "address".
In the case of the typical P2PKH address that you commonly see with bitcoin (the addresses that always start with a 1), the requirement that the output is encumbered with is that the future spender MUST supply a digital signature that can be validated with a specific public key. The instructions that explain this requirement are called a "script". That script is then encoded into the address that you use.
When you tell someone your address, and they type it into their wallet software, the software has been programmed to use that type of address to create the appropriate output script that you will be able to satisfy since you control the private key and will be able to generate the necessary digital signature when you later want to spend that output.
If someone uses an "address" that wasn't properly generated from a private key, then the sending wallet software will create a requirement that nobody will be able to satisfy (since nobody will have the private key and therefore nobody will be able to create the necessary signature).