You need host networking enabled to boot via the network. Check here for prerequisite configuration.
VirtualBox is capable of network boot, and is practically indistinguishable in configuration as compared to a real machine. To PXE boot a VirtualBox guest OS open the settings of a guest OS:
Click the system tab:
To enable PXE boot you have to configure the following section:
Then use the up and down arrows to set the priority of the network boot feature, as shown above.
You can create a guest OS that has no hard drive; there is no need for one. In such a configuration make network boot the first on the list.
Since you intend to use PXE boot, you may consider setting up a LTSP server.