There are several studies stating it is an inflammatory disease which would link RA and gum disease. RA produces high oxidative stress and gum disease is likely caused by Vitamin C deficiency which shows an oxidative stress situation.

Take a look at Vadik Brahmi Amla hair oil, it has tumeric along with other herbs - reports show some good results, it has no funky chemicals in it - looks 100% natural.

Hair growth depends on general nutrition, so a lack of vital nutrients will hurt hair growth.