At least given today's technology, rapid economic growth does lead to more global warming (assuming that scientists are right and global warming is caused by human activity). This happens in two ways.
For one thing, most economic activity requires the use of energy. As more factories are built, for example, more electricity must be used to run the factories and more fuel used to move things to and from the factories. All of this causes more greenhouse gasses to be emitted.
The second effect comes from the new-found economic prosperity enjoyed by the people. As they become richer, they come to want more things. They want new electronics which create more demand for electricity. They want cars, increasing the consumption of fuel. They want to eat more meat, thus increasing the number of animals that must be fed as they grow to edible size.
Until we find ways to create energy without using fossil fuels, there will be a connection between economic growth and climate change.