Perception and interpretation can very much be influenced by language (Sapir-Wharf hypothesis), so to the extent that perception and interpretation influence intelligence, it's not clear that the relationship is only in one direction.
- Sapir
It's hard to take these discussions on cognition and intelligence seriously when there is so much lossy compression going on.
For domains built primarily on linguistic primitives (legal writing), we do often reason through language. In other domains (i.e spatial) we reason through vision or sound.
We experience this distinction when we study the formula vs the graph of a mathematical function, the former is linguistic, the latter is visual-spatual.
And learning multiple spoken languages is a great way to break out of particularly rigid reasoning patterns, and as important, countering biases that are influenced by your native language.