Very much possible yes. The banana trade in particular has a sordid history.

Here is one about striking workers masacred: https://en.m.wikipedia.org/wiki/Banana_Massacre

Or there is this Guatemalan coup d’état which was lobbied for by United Fruit Company: https://en.m.wikipedia.org/wiki/1954_Guatemalan_coup_d%27éta...

So, yes. I think it might just happen that buying banana from somewhere keeps them poor. These are so well known cases that I somewhat suspect you asked the question as a softball.

> I think it might just happen that buying banana from somewhere keeps them poor.

What would happen if there was no market for those bananas?

Then they don’t get masacred to force others to labour on the banana plantations, and their democraticaly elected leaders don’t get overthrown by the CIA.

Maybe they find other ways to thrive, maybe not. Banan is not the only thing they could grow, and growing things is not the only way to make an economy work.

This is not an abstract economy problem from a econ 101 textbook. History cannot be rolled like that back and “what-if” is not a question we can answer.

What we know is that violence has been commited with the direct goal of securing said banana supply.

Would boycotting bananas help or make it worse for people in those countries?

It depends. In ideal conditions it wouldnt, but there's all sorts of ways that a large country like the USA (or its corporations) can keep a smaller country (and/or its poorer citizens) in poverty while trading with them, to their own advantage. e.g. Banana Replublics (https://en.wikipedia.org/wiki/Banana_republic), third world debt in the 80s/90s, poor people being pushed into growing cash crops instead of food ( https://www.washingtonpost.com/opinions/behind-africas-famin...)

I recommend reading about the term Banana Republic.

Bananas particularly are a case where this is blindingly obvious.

Please elaborate. How would stopping banana cultivation help any of those countries?

Historically it would have meant avoiding a coup of the locally elected democratic government (see https://en.wikipedia.org/wiki/Banana_republic).

To be fair, it's not clear whether it would have had any impact by the late 20th century.