If it is, this would be indicative of
a compromised head gasket, warped cylinder head, or damaged oil cooler (if the car uses radiator coolant for cooling the oil).
A fine crack in the exhaust manifold or
compromised head gasket could introduce oxygen to the exhaust stream.
There are so many things that could explain slow overheating
A compromised head gasket is just one of them.
Not exact matches
If the
head gasket leak is introducing gasses, hot gases at that, then I can definitely see the cooling system greatly
compromised as you say.
So, to answer you question very broadly, yes, a failed
head gasket can lead to overheating by allowing the cooling system to be
compromised.
Yes, it is possible for the coolant to leave through the exhaust, if the
head is warped or the
head gasket is
compromised.