No research has yet proven if houseplants help with climate change (by taking carbon dioxide from the air) or contribute to climate change (due to the processes related to growing, transporting & selling them).
However, some houseplants can survive in drought. Researchers from the Natural History Museum of Denmark and the Department of Plant and Environmental Sciences at the University of Copenhagen, have in collaboration with researchers at the Royal Botanic Gardens Kew in England, demonstrated that certain Aloe species preserve resources during drought.
Plant biologist Louise Isager Ahl of the Natural History Museum of Denmark says in “Houseplants Ability to Survive Drought Can Provide Useful Knowledge for the Climate Change Era” (University of Copenhagen, 2019):
"I can imagine that by identifying and understanding the genetic mechanisms allowing Aloe species to fold and unfold their cell walls, we will be able to integrate similar mechanisms into crops to make them more resilient to climate change,"
So even if houseplants are not combating climate change, they are helping in research to combat climate change!