Would Churchill offer Iceland to the United States?

Would Churchill offer the United States responsibility for Iceland in this scenario?

The historical arrangements already moved in that direction: British and Canadian forces preceded an American takeover in 1941, before US entry into the war.

British forces occupied Iceland before Canadian forces helped hold it. American forces then assumed responsibility in 1941 while the United States remained formally outside the war. The historical sequence already provided a precedent for transferring an Atlantic defence commitment to the Americans.