I have yet to see any feeder insect chew their way out of a frog. Insects breath through spiracles in their exoskeletons, if you cover these pours, an insect will suffocate. The inside of a frog is very wet, so when a frog swallows an insect, it suffocates and dies. Then there is the frog's stomach acid which will also kill said insect. So no worries.
Do keep the feeding of mealworms and other beetles/hard-shelled insects to a minimum, as too much chitin (the material in their exoskeletons) in a frog's digestive tract can cause a GI impaction, which can lead to a frog's death.