Here's an interesting paper on the topic: https://files.eric.ed.gov/fulltext/EJ688443.pdf
And its replication: https://www.tandfonline.com/doi/full/10.1080/07421656.2012.680047?scroll=top&needAccess=true
It looks like structured coloring (following pre-stablished line boundaries) can help reduce acute anxiety, but unstructured coloring doesn't appear to have the same effect.
Unstructured drawing, does appear to help alleviate the symptoms of stress (as an example, a study with PTSD patients: https://pdfs.semanticscholar.org/3f53/0ad817fb4597a1b755ae98daa839a167f2b9.pdf )
As for art-therapy in general, its therapeutical properties have been explored in the past years, medical daily has an approachable blog entry about this: https://www.medicaldaily.com/therapeutic-science-adult-coloring-books-how-childhood-pastime-helps-adults-356280
I would say it can be effective, but I wouldn't recommend using it as a "stand-alone" treatment for severe stress disorders.
Coloring to relieve stress can also be done digitally. I have several programs on my phone and computer that I use to color. This is a helpful self-care strategy!