Yes. The Linux server can serve multiple roles. If your network does not already have a DHCP server, it can be done. NOTE: Most consumer routers have a DHCP server activated by default. Having two DHCP servers on the same subnet is not really a good thing (without a special configuration, but I digress).
Linux also has a TFTP server that can be setup to hold the configuration files.
Both of the services are completely independent of Asterisk. There are tons of documents on the Internet about setting up DHCP and TFTP and are out of the scope of these forums.
Also, different phones have different requirements for directories. The file format needs to be correct for the phone. There is nothing in Asterisk that will generate the directory for you, you will have to do that yourself. On a small system with little changes, this can probably be handled in a text editor. Larger network would need something else. There may be some third party applications that you could use, search the Internet and see what you come up with. Some phone vendors also provide a tool.
Telling the phone sets where to find a directory is also phone specific. DHCP will not tell the phone where the directory is. It will tell the phone where to find the config file which contains, among other things, the information on where the directory is.