Your question is very interesting, and I can answer I from two points first your question point
Do you think that Orthodontic treatment affects periodontal tissue?
Answer is absolutely yes ,orthodontics treatment is directly connected to the periodontics ,I give a lecture about 4 hours to my graduate students in orthodontics about biomechanics of tooth movement and you can tell you that the periodontal ligament is directly affected by the orthodontics treatment .I can suggest for you two publications one is a chapter in dr. William profit book contemporary orthodontics on the bio- mechanics of tooth movement where all these e questions are answered. These answers are mostly on the level of Histological changes and blood vessel changes in the periodontium.
I also can suggest for you my publication entitled : Molecular Biology of tooth movement by Galil et al. here the paper discusses not only the histological changes in the periodontal ligament but also the molecular changes like growth factors and molecular transcription and stimulating factor ,I have up loaded my paper so that you can read it.
The second part of this reply is that there are many studies on the effect of orthodontics on periodontally diseased teeth and to summarize this point I included a summary from a thesis by the same title which I also uploaded
Studies on orthodontic treatment in subjects with periodontal disease
Zasčiurinskienė, Eglė
Jönköping University, School of Health and Welfare, HHJ. ADULT. Department of Orthodontics, Medical Academy, Lithuanian University of Health Sciences, Kaunas, Lithuania.ORCID iD: 0000-0001-8364-0510
The conclusion of that thesis abstract is
conclusions: Based on the results of the present research it can be concluded that periodontal-orthodontic treatment under optimal conditions (experienced clinicians and patients with excellent oral hygiene routines overtime), if needed, could be included in the rehabilitation of patients with periodontal disease without deleterious effects. However, there are two important prerequisites: meticulous personal oral hygiene of the patient and optimal sub-gingival control of inflammation before and throughout the combined treatment.
I have included here for you 3 references to support my answer as an attachment
I hope have I have helped .
Dr.K.A.Galil.Professor of Dentistry DDS.,D.Oral & Maxillofacial Surgery ,PH.D,FAGD.,FADI.,Cert.Periodontist(Royal College ) Departments of Periodontics,Orthodontics and Clinical Anatomy Schulich School Of Medicine and Dentistry. University of Western Ontario London,Ontario. www.drgalil.ca