Answer from Lawrence E. Gibson, M.D.
No — shaving hair doesn't change its thickness, color or rate of growth.
Shaving facial or body hair gives the hair a blunt tip. The tip might feel coarse or "stubbly" for a time as it grows out. During this phase, the hair might be more noticeable and perhaps appear darker or thicker — but it's not.
Consult your doctor if you notice a sudden increase in facial or body hair. This could be a medication side effect or a sign of an underlying medical condition.