Unertl started his scope company in 1936, with scopes on the market in 1937. Most records were destroyed on Unertl's end, but 3,500 scopes were purchased by the USMC. 1,750 were accepted as of April 1945. The rifles were mostly build on National Match rifles, which there was said to be 1,047 in USMC inventory at the beginning of 1942.
First shipment of 150 to 250 Unertl scoped rifles were delivered to First Marine Amphibious Corps in December 1942. There were also M1903s in the theater with Lyman 5A or Winchester A5 scopes.
Prior to the end of the war (August 1945), the USMC ordered that there would be 108 sniper rifles (specifically the Unertl scopes rifles, M1903A4s, and M1Cs) allocated to each division. I don't know what division strength of the USMC was at that time, but simple multiplication would see what they wanted. The Unertl rifles were still being used then, but would be replaced with M1903A4s and M1Cs as need be. The Navy did take some of these rifles (400 in an August 1945 request) for mine clearing.
When the Korean War began, the USMC was to adopt the M1C, but testing was not completed by the start. So old Unertl scoped rifles were issued with M1903A4s that were supplied at the end of World War II. However, more Unertl rifles were assembled from standard service rifles to keep up with demand. These were used until the end of Korea, but the adoption of the M1C put it out of service.
From 1942, Unertl scopes were prominently attached to M1903s. However, some were attached to Winchester 54 and 70 rifles during World War II... just not official use. The books do say that scopes were removed and used on Winchester 70s, but as was the case with the Winchesters in World War II, there could have been M1903s with Unertl scopes floating around in Vietnam. I have seen pictures of Winchester 1897 shotguns there, so a M1903 isn't that far off. But once the sniper role was being established in Vietnam, I'm sure the latitude for non-standard arms was cut. That is my opinion on it (regarding Vietnam), though... nothing more.
That is just a little bit about the rifles that I quickly pulled out of three books on the subject. Peter Senich wrote The Complete Book on US Sniping and US Marine Corps Scout-Sniper. Joe Poyer wrote Collecting the American Sniper Rifle 1900 to 1945. If you are interested in the subject, I do recommend them. In regards to images, you'd have a crap load with the three books. World War II and Korean action shots, training, and then documents/informative shots. The three that I really liked were all Korean War images, and all with the Unertl scoped M1903s. One paired with a M1C, another supporting a Browning M1917 machine gun, and the last with a BAR spotter. If I get ambitious tomorrow, I'll see if I can post them up.