Yes! To collect informations about domains (URLs / FQDNs) visited, the traffic must be directed to a program that analyses the packets.
SARG only samples web proxy accesses.
In times of encrypted internet traffic (HTTPS, …) it may be a bit tricky to sample information about URLS visited. Mostly the transaction is [lookup the IP by DNS] → [authenticate and exchange keys] ->[communicate using TLS], where the proxy isn’t involved to much.
Communications besides HTTP(S) are not logged by the proxy. Logging DNS request may help, but includes queries not used for communications.