Well, if you want to view it as part of the treaty clause (which it hasn't been--you don't see the Senate approving it by 2/3's votes)--then it all boils down to another question: Was the Louisiana Purchase constitutional? (ie does the enumerated powers section even apply to treaties?)
A case can be made that it doesn't, since treaties are not normal pieces of legislation--they are negotiated by the President, not drafted by Congress--the Senate is simply ratifying the treaty, nothing more.
Questions like this are where I get a bit ancy, personally--as I'm a libertarian domestically (economically more so than socially), but when it comes to foreign policy, no way. And that's the major reason I still consider myself a Republican, not a Libertarian.
Foreign aid isn't charity--it's a tool to further the interests of the United States (well, that may have come off wrong, but you know what I mean)--qv the Marshall Plan.
The Louisiana purchase was unconstitutional and as I recall Jefferson himself lamented the fact that he had violated it. But that happened two hundred years ago and we can't change it now. However, that doesn't mean that its OK for other presidents to violate the constitution. That would be like saying O.J. Simpson got away with murder so now anyone can commit murder.
As far as treaties go, yes they probably could be used to create legal foreign aid plans, but I don't think the founders intended it that way. And as you point out no such treaty has been signed.
When it comes to foreign aid for security, such as our support for Israel, possibly that can be justified as defense. But when it comes to situations such as the tsunami disaster, I think the government is overstepping its bounds, despite the humanitarian nature of it. Whats wrong with allowing the people to decide how much they wish to spend on it?
One of the reasons I object to government violations of the constitution is that the constitution is the fundamental law of the land. It defines the government, limits the power of government, and protects your rights and mine. Without the constitution our government could become the worst form of tyranny imaginable. When government is allowed to violate the constitution, even for benevolent purposes, it opens the door to further violations, some of which might not be so benign. We should not fall asleep at the switch and assume that government always acts in our best interest. We should be vigilant and hold their feet to the fire when it comes to the constitution.