Aww wow thats cute!
Short answer is no, But my DD is old enough to damand it when she wants it.
Its totally fine to leave him while he's happy to just gaze around. DD used to get so over stimulated at that age but was quite happy on her mat for 10-20 mins.
You can get him one of the jungle gym mats, the ones that have a kind of mobile of toys hanging over the top that Im sure he'll be fixated with
also DD used to love a quick trip around the garden at that age too.