When a VirtualBox VM's Adapter is set to NAT can a VM access the Host computer?

In a VMs network settings:

1. Right click settings,
2. then in the resulting Settings dialog select Network from the side bar
3. And click any Adapter N tab,
4. If I set the Attached to: drop down to NAT

Will the VM be able to access the host machine? Does it get a specific IP with NAT?

It depends on what you specifiy as access and what you configure for it.

Using NAT is like placing the VM in its own network and put a router in between it.

This is similar as to how your computer is shielded from a computer on the internet. Any computer on the internet that wants to have access to your pc needs their ports to be opened. Through VirtualBox's NAT interface, you can configure ports that have access from the outside to the VM and back.

More information can be found if you press the help button on the bottom right, and in the search type NAT.