Use the Airdrop network to access a computer?
Yes, the VNIC created when an AirDrop window is open can be used by any application. AirDrop simply runs Bonjour (mDNS/DNS-SD) on that interface to discover peer and the TLS to transfer files. Any network application that can be configured to use a specific interface and supports IPv6 should work.

For example, pinging (replace X with whatever the interface number is in use, see ifconfig for example): ping6 -I p2pX ff02::1