Most likely he will be held under what is called a "detainer" which will keep him when his sentence is completed in Fulton, then the Whitfield sheriff will take him into custody to face the pending charges. If this warrant is not related to the charge he is doing time for, it is unlikely he will get "time served". But it really depends on the charges and how pissed off the prosecution is.
https://www.inmateaid.com/ask-the-inmate/my-husband-released-date-is-in-nov-of-2015-he-has-a-warrant-in-whitfield-county-he-has-been-in-jail-in-fulton-county-since-nov-15-2014-and-been-in-prison-since-july-4-2015-do-u-think-he-will-get-time-served-and-released-from-whitfield-county-jail#answer
Accepted Answer Date Created: August 15,2015