I have never tried to do what you suggest, but banks might consider the same type of permanent income that the goverment dows in order to apply for a rentista visa (basically a visa for retirees who do not plan or working). http://www.expatperu.com/legalities/wha
... ista-visa/ , however, in previous posts memebers have stated that they have always been turned down. Banks are all about managing risks here.
As another poster mentioned, if you have the way to take a loan from the US in order to pay in cash here, you will 1) get a better intreres rate; 2) you will be able to negotiate a better purchase price with cash in hand; 3) you will save yourself a ton of anguish.