No never! I have no idea why this misconception exists.
If you have bleach applied to your hair and it causes damage (also incorrectly cared for following) it could cause breakage (perceived as hair loss often) or in a very small cases a burn to the scalp.
You could be unfortunate enough to have a reaction to a tint applied in the salon or at home (although in both cases a patch test should have been carried out 24hrs before hand). This may result in an itching or burning sensation on the scalp- usually whilst the colour is on or in the hours that follow. An anti histamine should be taken and Aloe Vera is a useful product to apply to relieve the sensation.
The reaction may calm down of its own accord, but is usually described as a form of Dermatitis. But still, not cause hair loss.
A Trichologist can help to diagnose your condition, at Sussex Trichology we can treat this successfully with a combination of clinic treatments and home use products combined. In majority of cases, we are completely against the use of hydra cortisone for these reactions.