Device CAL for each server put in place

I currently use Server Device CALs because we have multiple people who use the same computers during a 24 hour period (Hospital...nurses and physicians).  I currently have approx. 800 computers on the network and over 1200 users.  I have about 850 Device CALs.  As I add more servers, I don't need to purchase another 850 Device CALs for each server, correct?  Does the single Device CAL allow access to all of the servers in my domain (single domain)?  Thanks in advance