No.

Paper bags don't add up to much. The Indians use vast numbers of small bags. I weighed a paper bag I got some fruit in just now, 7g. Divide by x to compensate for realistic recycling. A tree weighs several million grams. Not all of it becomes paper, but still, one tree is a lot of 7g bags.

Adding to that: Once the paper is burned or rots, the route back to a new tree is fairly short. Not like plastic, which forms new oil in fifty million years.

I was about to write that certified timber has a great sustainability record. You can recycle all of it and when it regrows it does so by pulling carbon from the atmosphere. But when I read the WP article [1] on sustainability of paper I saw that the actual problem seems not to be in the wood used, but in other pollutants released into nature when producing paper.

[1]: https://wikipedia.org/wiki/Environmental_impact_of_paper

Not really, new paper is mostly produced from recycled paper. What destroys the jungle is deforestation to create farmlands.

It is my understanding that paper isn't made from jungle tree species. An increased demand for paper would lead to an increase in tree farms in temperate climates, not tropical.