As someone who sends back thousands of dollars a year to family in Russia and Lithuania: they're sure as hell not spending it on American products. They spend it on food, medicine, housing, and education which are all sourced locally except for a tiny fraction of products that can't be (mostly IP restricted things like medicine, textbooks, movies). Once in a while they'll buy a computer manufactured in China from an ostensibly American company that rarely repatriates their profits.
The problem is that most American exports are luxury goods (even in agriculture) and when you come from a poor country where a few hundred dollars makes a huge difference, those exports will account for a tiny amount of the capital sent there. There are many long tail benefits but I doubt they are quantifiable enough to say that the drain from remittances is anywhere near break even.
Edited to add: my family doesn't even need the money, despite having health conditions that would economically cripple someone in the US without the best insurance. Salary + pensions + free education and healthcare are enough to survive so most of the money I send them are to give them breathing room and spending money. I think half of what I send them gets spent on spoiling the younger family members and the rest goes into a rainy day account. The only time they "spend" on American products is when one of us in the US buys them iPads/iPhones (on top of the remittance) as gifts on one of our visits and they buy a $5 game twice a year for the kids to play.
That said, if Americans knew how much of the >$100 billion remittance market went to buying little kids books, candy bars, sports equipment, and board games, they'd think the money was worth all the happiness it brings.