It'd be really difficult to see either a Germany capable of that sort of power projection or a United States that somehow intervened more severely than it already did during the 1920s. Roosevelt's 'Good Neighbor' policy was more a reaction to that and the challenge of the Great Depression than anything else. There's also the factor of Germany having their hands full securing their positions in Eastern Europe ensuring Brest-Litovsk becomes the status quo and Africa as they won't have lost their colonies and might possibly get a few more at France's expense.
The 1916 Defence Act was already a step in the direction Wilson feared; doubling the size of the Army and NG, giving the NG money for much more training, forming the ROTC, buying 375 planes, 10 battleships, 6 battlecruisers, 10 scout cruisers, 50 destroyers and 67 submarines.
I don't think Wilson was expecting major battles in Latin America the day after the war ended or anything that drastic, certainly the Military and Naval expansion authorised in 1916 had a 5 year schedule for completion. Rather I think that instead of a benign Britain in effect enforcing the Monroe Doctrine the US would have to deal with Germany who might well do similar interventions as the US in support of its business interests, or picking sides during instability and supplying assistance to that side during the 20s.
Because they are currently occupied by the British and until they're dictating terms in London, Britain's the one negotiating the terms on their future.
That will be the case because the Germans will have:
- defeated the BEF in France, possibly capturing a large part of it and having a large part flee back to Britain without its equipment
- will occupy the Belgian and French channel coast
- will be shelling Britain with Langer Max guns and bombing with planes
- will have broken the blockade by having access to the food of France and Spain
- will have uboats and other naval units operating from Le Harve and Cherbourg
Britain will gladly hand back Germany's colonies and throw in a few more to end this state of affairs.