The EU already has a land border in the Americas. French Guiana is part of the union and it touches Brazil and Suriname. So the gate is already open to work it from the south up instead of the north down.
I read somewhere -- great source, I know -- that the existing rule is that the country has to be in Europe, though, not that it has a border. Otherwise Malta, Ireland, and Cyprus would not qualify, and the UK too back when they were in.
Oddly enough, the Canadian/Danish border is a questionable one for this purpose anyway -- Hans Island (where the border is) is part of Greenland and Greenland is not in the EU. It left in 1985 and is now one of the "Overseas countries and territories" that have special rights in relation to the EU but are not actually in it.