No client does not need to be open for receiving transactions.
You do not have to open it for as long as you like. Just make sure that if you make a wallet for backup reasons to generate enough receiving addresses in advance, because if you make new addresses on a running copy that are not in backup they most likely wont show up when you run backup copy.
Has anyone tested this?
I thought wallet.dat was just a key to cash out only and all other data is stored on the global p2p network?
Just when I thought I understood how this works, Now, im confused again.