Does caramelizing increase the amount of sugar in a dish?
No, neither caramelization (which is the same as pyrolysis in this context), nor the Maillard reaction increase the sugar content of onions. They actually decrease it a bit. 

Caramelization/pyrolisis starts out with a sugar and ends with something that is not sugar. Maillard starts with a sugar and amino acids, and ends up with something that is no longer sugar. So in both cases, sugar is being used up and makes something which is not, chemically speaking, sugar. 

This is the answer to the literal question you are asking. Since health questions are off topic here, I will only briefly mention that "fast carbohydrates" and "sugar" are not necessarily the same thing, and that the effect size could or could not be physiologically significant. So, this information alone is not sufficient for you to draw conclusions about the healthiness of eating caramelized vs. noncaramelized onions.