That will depend on what server configuration you are talking about. Most server cannot detect/record remote MAC (Media Access Control) addresses since MAC is use in the data link layer (that means use by network interface cards, routers etc) mainly for error correction and collision detection purposes.
A web server will only need to know your ip address and port number to send you the information you requested. Whether it wants to record ip addresses or not is optional. It does not need to know your MAC address at all.
A file/database server normally only record the users login/logout timmings, ip address and the transactions made.
And just like IP address, MAC address can be changed. Any recorded MAC information will be USELESS if you change network device or changes the device MAC address. Thus it is quite pointless to record MAC address in most cases.
However, I do know that St@rh*b MUST keep a record of MAC addresses in their network servers at all time for some reasons which I cannot post...
So the answer to the question
Do servers log that MAC addresses as well?
-> No