All paid-for upgrades (LR3, LR4) have their own serial numbers.
The installer detects a full version or upgrade via the serial number.
Having LR3 already installed merely means that the LR4 installer does not need to ask for your LR3 serial number. It does not mean that LR4 does not require a serial number to be entered.
If no prior version is detected then, after you have entered your LR4 serial, then the LR4 installer will ask you to enter this serial from an earlier qualifying version, in your case LR3.
To address your question, you must have an LR4 serial number in order to install LR4 so there must be one with the packaging.