This works fine. The bitcoins will appear next time you start your wallet application. Bitcoins are not actually received by the software on your computer, they are appended to a public ledger that is shared between all the devices on the network. If you are sent bitcoins when your wallet client program is not running and you later launch it, it will download blocks and catch up with any transactions it did not already know about, and the bitcoins will eventually appear as if they were just received in real time. Your wallet is only needed when you wish to spend bitcoins.
Well said. The benefit of using cryptocurrency is the security and convenience in comparison to physical money. This has to be one of the many features that support it, or else no one would actually use and the value won’t be this high at the first place.