Naps in stroller

I know babies shouldn’t stay in the car seat on the floor, however.... can my baby stay in the car seat in the stroller if we are out and about?

For example we run errands or have gone for long walks or to the mall and the baby is in the car seat and in the stroller. We have the graco click connect that goes into the stroller. Is this safe for them to nap in if we are on the go?