That would be most likely. The US would be hugging the coast and refusing to move inland. Just like EU3 AI.
In all seriousness, it still comes down to how you extend it. Perhaps Santa Anna isn't injured as early in the Pastry war, and fighting continues long enough (and importantly, the blockade continues long enough) that the RRG could establish themselves. He could be injured later to have the same effect, or he could come out unscathed. If that happens, though, his efforts to return to power will have to be greater, as he used his war wound as part of creating his new image in his return to power.
Note that the US supported the French blockade, sending a token frigate to help interdict any ships trying to break it. So the US already had given France its support.
Actually, they'd enter the US as states, not territories, if they are independent and petitioning to join. It's the court's decision to adjudicate disputes between two sovereign states. Granted, I imagine that in any scenario that the Rio Grande would be granted Tampico and all territory north of the border west to Zacatecas, if that is the final eastern border line.
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Edit: Found this in the Map Thread. It's relatively current, but it's a good map to get an idea on the distribution of Mexican urban areas.