As for the question - yes, this functionality is designed exactly for this purpose. You're device will report custom hostname to DHCP server when obtaining address. If your DNS server can use DHCP database for resolving hostnames (like most home wifi routers), you should be able to use this hostname instead of IP address. The actual hostname will be made by concatenating the prefix set in config/lwipopts.h with hexadecimal representation of 3 lest significant bytes of MAC address.
If you have any problems, let me know here or open issue on github.