Lets say company X announces on September 22nd (before market opens) that all stockholders as of that date have the right to purchase additional shares at a discount. Does it makes sense to become a new stockholder on that day (assuming the price will go up in the future) in order to be able to participate in the offering ? Is there a delay between when the stock is bought and when new stockholders appear on the company stockholder list ?
Yes, there is a delay between when you buy a stock and when you actually take ownership of it. This is called the settlement period.
The settlement period for US equities is
T+2 (other markets have different settlement periods), meaning you don't actually become a shareholder of record until 2 business days after you buy. Conversely, you don't stop being a shareholder of record until 2 business days after you sell.
Presumably at some point in the (far) future all public markets will move to same-day changes of ownership, at which point companies will stop making announcements of the form
all shareholders of record as of September 22nd
and will switch to announcements of the form
all shareholders of record as of September 22nd at 13:00 UTC