(Presumably this sentence occurs in a context where we already know who "he" is.)
The comma is a problem in this sentence.
If the meaning is meant to be as follows...
She got words of caution at home. These words of caution suggested that "he" could be
a fake[etc]. She flew to India despite getting these words of caution.
...then the sentence should be written WITHOUT the comma after "home" and should have a comma after "India". This is because "words of caution" is a noun (nominal) phrase that is modified by the two adjectival phrases "[that] she got at home" and "suggesting he could be fake or a con man[etc]". These two phrases modify the noun phrase "words of caution". They are directly connected to it and should not be separated from it by a comma [despite the awkward length of the phrase].
As the sentence stands now - with the comma - its strict grammatical meaning could be that while Adriana was flying down to India she spent her time on the plane suggesting (presumably to other passengers) that "he could be fake or a con man, etc."
Alternatively it could mean that (somehow in the story's context) the fact that she flew down suggested that he was a con man.
The sentence might better be written:
"Despite all the words of caution she got at home suggesting that he could be fake or a con man, Adriana flew down to India."
But it might be best to avoid syntactical ambiguity and just separate the thought into multiple sentences:
"Adriana's family cautioned her that he might be a con man or worse. Despite their warnings, she flew down to India."
I hope things work out for Adriana. I'm beginning to worry a bit.