One good consipiracy theory deserves another. Honestly though, I teach a history class that is a survey history of WW II. Off the top of my head I cannot remember the answers to the following questions, but they will help give background.
Yes, the United States was not at war on the date listed.
However, FDR was well on his way to trying to overcome the isolationist feelings in the nation and successfully convinced Congress to appropriate what was at that time, the largest ever appropriations bill for military spending while the nation was at "peace." FDR believed that the United States not only had to enter the war on the side of the Allies, but would be drawn into it whether or not the U.S. wanted to.
The lend-lease program was well underway, and don't ask any American Merchant Marine personnel whether or not the U.S. was at war with Germany. They had been dealing with u-boats since the start of lend-lease.
A really key question, which I cannot look up, all my books on the subject are locked away in my office at school, is when did plans for the Manhattan project get underway. Not when the acutal Los Alamos facility was built, but when the plans for the start of the project got underway.
This was a 2 billion dollar project that had nearly every state in the union involved in some way or another. If the mystery operations occurred after the start of this project, then I think it might be feasable. If the actual order from FDR to start the Manhattan Project came after the mystery operating period, then it is highly unlikely.
Einstein had already immigrated to the United States and had contacted FDR about the theoretical and practical possiblity of an atomic bomb. Find the date of when things got started, unofficially, secretly, etc. and you may very well have the answer to whether or not this was possible. The Manhattan Project was VERY secret and took lots of work in many locations.
Given what I know about many seemingly innocent happenings during WW II, this is possible. Or, if nothing else, another good conspiracy theory to research.