Yes, but keep in mind that while Patagonia may not have been occupied by other powers, it was not necessarily up for grabs. Spain (including its viceroys in Rio de la Plata and Chile) would almost certainly mount an expedition to destroy the colony. They sent a fleet to confront the English over the Falklands; Denmark and Sweden were much less risky opponents to challenge. Later in the 19th century, Argentina is also too strong to oppose and, will eventually occupy the territory outright. For a country to establish a colony, it must occupy the territory and defeat the Spanish or Argentine counterattck, something that would be very difficult to do alone.
This is based on the assumption that Sweden or Denmark would establish a formal imperial outpost. I suppose an initial settlement of simple farmers could be set up there provided it declared loyalty to the government in Buenos Aires. Then, after the colony grew, it might try to break away so it could be annexed by the mother country or perhaps simply independent.
Another thing I thought I might mention is that there were Indians living there. How effectively those people would be able to resist determined invaders is unclear but I seem to remember that they had a reputation for being fierce. Conflict with these people could be a bit of a deterrent to settlers. Then again, who knows how they would interact.