Can thin people with high metabolisms experience the same health problems as overweight people if they eat unhealthy foods?

Often, yes. Obese people can have more illness', but on a whole yes, either obese or thin people can have the same diseases. Example: An obese person could have heart problems due to the extra weight carried around and lack of exercise (getting the heart rate down) but a thin person that doesn't eat well or could be Anorexic could have heart failure as well. Yes, thin people with poor diets can have terrible heart health and poorly regulated blood sugar, they just don't eat as much as it takes for them to be fat. The reason why being thin means you're MORE LIKELY to be healthy is because thin people are willing to eat less, and eating less/being hungry is better for regulating cholesterol and blood sugar, and can also help stabilize the immune system. That is, thin people can "get away with" more sometimes.