No. In the past, there was speculation that mice went outside to locate drinking water after they consumed rodenticide. This started when some of the early rodenticides caused mice to become thirsty. This is just not true with modern rodenticides. After mice consume an anticoagulant rodenticide, their capilaries become damaged and they die of internal bleeding. Depending on the active ingredient, the mice die within 3-10 days upon consumption.
Regardless if you treat mice with rodenticide or if they die of natural causes...many probably do not go outside. Mice only live about 1 year, and many people have had many generations of mice in their attic.