is it possible to get someone else's address or will it be skipped?
Theoretically it is possible, but in reality it will never happen. There is certainly no mechanism or database that wallets or exchanges use to check if an address has already been used when generating new private keys.
The reason it will never happen is simply down to math. The numbers we are dealing with here are unimaginably large. For example, if every human on the planet each generated 1 million new addresses every second, and had been doing so since the birth if the universe 13.7 billion years ago, we would only have generated approximately 0.0000000000002% of all possible addresses.
This is really some deep stuff. I used to get bothered the same way
noorman0 was and would always crosscheck to see if my transactions actually landed in my account on exchanges. Even on this forum when new entrants are asked to pay a fine for "IP cleansing", I used to wonder how that particular generated address is specific to that account. Now I know. Thanks buddy for your explanation.