Yes, you can bait and distract the US (if they go for it) but what of the Commonwealth? By this time they have surely activated Brazil and will be able to check the move. The Commonweakth presence ups the ante for the Axis. It’s very possible in this case to go from “leading the dance” to performing the funky chicken when resources needed to attack/defend victory cities–- none of which are located in the South American theatre— are tied up fighting easily reinforced allied “gimmie” armies. If you throw in another 15 IPC investment for an airfield (Rio de Pro or otherwise), you might as well make the diversion into a full blown gambit to drive right on up to the USA and take them out.
Again, I’m not saying the Argentina activation doesnt have its place but I’ve always seen it from an opportunist point of view. If it looks like the Allies are weak in the theatre and I can exploit the opening without compromising other, more important, theaters, I’ll consider going for it. If it looks like there’s not enough return for the expense (which is usually the case) I won’t bother. The S. America is just too logistically distant and costly, especially as compared to the Allies, for me to bother with very often. You can’t build a minor IC anywhere on the continent. There isn’t even one naval or air facility to capture. A real PITA to get anything outta.
As for Red Dawn, the more nothernly American climes represent a much more practical and logistically viable theater for that scenario to play out. Maybe S. American operations in support of hitting N. America would be worth looking at.