Hello Mike.
I've been looking into early US Navy aviation for awhile now and other then the 2 serial numbers you listed as belonging to Sopwith Pups I haven't found a thing about Pups serving in the US Navy. From my research I have found that the USN only used 4 types of aircraft to launch off of US Battleships...the HD-1 (10), Ni28, Sopwith Strutter, and the Camel.
The first launch of off a USN BB platform was a Camel flown by Lt. Cmdr. McDonnell USN, on March 9 1919 at Gitmo Cuba. It seems the Camel was only used in testing and training and was not to be part of a future ships company-one Ni28 and one Strutter were the planed BB complement.
In 1921 the compressed air catapult began being used on the BB's and by 1922 the launch platforms had been removed from the BB's. 1922 also saw the launch of the USS Langley as CV-1. Because of the use of radio receivers used on the Strutters the Navy now turned it attention to using the catapult launched aircraft in the Scouting role. Ships that did not have room for catapults were forced to lower raise and their Scout with a winch.
I'm afraid I don't know the meaning of the USS Idaho 1926 Cuba reference by another poster. At that time the Idaho already had its catapult system in place, its turret launch platforms removed and was more than likely outfitted with Vought aircraft used in the scouting role.
I have added a few pics of the Idaho showing its change from launch platform to Type A and possibly to Type P catapult.

USS Idaho 1920 with its forward and rear launch platforms- I cant make out any aircraft aboard in this photo.

USS Idaho 1922 -If you look close enough you can make out aircraft and catapult at the stern and what I take as a launch platform on a stern upper turret.

USS Idaho 1925 underway in the Pacific stern catapult Type A or P.

USS Idaho- 1925 A good shot clearly showing stern catapult with what appears to be a Vought Scouting aircraft facing aft.

USS Idaho- 1926/27 Another great shot this time with 2 aircraft at the stern catapult.

USS Idaho-1926/27 A close up of the above picture, definitely not 'Pups'.
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