Yes, exercising can lower these levels. However, too much sugar in your body while exercising can be dangerous. According to an article by the University of Michigan's publication, Tips for Exercising Safely When You Have Diabetes, It's vital to watch your blood sugar if you're exercising, especially people taking medications to manage the condition.
Make sure not to exercise when you have high glucose levels or ketones. Additionally, anyone with diabetes should measure blood sugars before they begin an activity like running around and playing sports. If the individual has any of these symptoms: over 300 mg/dL or the presence of ketones, then it would be wise to wait until this subsides before trying such strenuous activities again.
However, just because you don't have diabetes doesn't mean you can't experience problems with high blood sugar during and after exercising. Too much sugar is harmful to athletes as much as it is for people who don't participate in organized sports.
Additionally, a 2016 study found that 4/10 of the participating athletes experienced a substantial amount of time above the 6.0 mmol/L level. The report's authors concluded that,
"Contrary to expectations, high BG appears to be more of a concern for athletes than low BG, even in those with the highest energy expenditure and consuming below the recommended carbohydrate intake."