Effectively no, first if you look at the picture there are holes on the sides and no body is putting the lid on.
More widely Cold CO2 from dry ice or pressurized tanks is a problem because it’s both releasing a lot of CO2 and that CO2 is very cold which means it sinks quickly. On the other hand babies breath is both fairly slow and has a relatively low CO2 concentration which makes it easier to mix with the air. On top of this breath is warm so combined with a convection current from body heat in otherwise still air it has a tendency to rise which improves mixing.
An extreme version of this happens when a baby or small child falls down a pipe and can avoid suffocating for hours.
More widely Cold CO2 from dry ice or pressurized tanks is a problem because it’s both releasing a lot of CO2 and that CO2 is very cold which means it sinks quickly. On the other hand babies breath is both fairly slow and has a relatively low CO2 concentration which makes it easier to mix with the air. On top of this breath is warm so combined with a convection current from body heat in otherwise still air it has a tendency to rise which improves mixing.
An extreme version of this happens when a baby or small child falls down a pipe and can avoid suffocating for hours.