It seems that the answer is yes, although British sovereignty seems to have been merely nominal, since no attempt was made to actually occupy the island. This 1961 article by H.E. Maude discusses the history within a regional context. I will summarise the main points.
The disputes between the United States and the UK following the American Guano Islands Act of 1856 fell into abeyance when the few commercially payable guano deposits were exhausted. From that point, almost all the islands covered by the American Guano Act were considered, in the absence of any active American interest in them, to be British possessions.
That situation changed when the strategic value of the islands in relation to trans-Pacific civil aviation was recognised. Baker Island (and also Jarvis Island) was placed under United States administrative jurisdiction by the Presidential Order of May 13, 1936; In March, 1938, Mr. Stephen T. Early, Secretary to President Roosevelt, announced that:
The position of the United States as regards lands or islands hitherto
unoccupied or in question as to ownership is as follows—
- First claim to title over undiscovered territory rests on discovery.
- Under this many islands in the Pacific were first discovered by American flag ships.
- The United States always has held that mere discovery does not give final title. If it is not followed up by reasonable occupation it
In relation to the islands in question, of which there are many, the United States assumes the right to occupation either because of:
(b) former occupation,
(c) failure of any other nation to occupy,
or a combination of the three.
I'd guess that events in 1939 rendered diplomatic discussions between the US and UK over the future of the islands moot, and Baker Island remains a United States possession.