Yes, engine oil and automatic transmission oil can both get into the cooling system.
Low engine oil can effect the cooling system as it creates additional friction which may be difficult for the cooling system to remove. The oil is designed to both lubricate and cool the internal components.
It will take a few flushings to get all of that solution back out of the to be oil in the cooling system so it probably doesn't have a lot of oil removal capacity.
A broken piston ring can allow oil to get into your cooling system. A bad valve seal can also allow oil into the cooling system.
Once you have determined and repaired how the oil got into the cooling system eg. head gasket , oil cooler, or turbo, you need to thoroughly flush out the cooling system with a chemical cooing system flush and plenty of water.
does cooling system hold pressure?
That's not the question you need to ask yourself. There's not supposed to be any oil in your cooling system, so you need to take your truck to a diesel service and get it fixed.
The cooling system in the 198 Expedition includes the radiator and its reservoir along with the thermostat. This system included an oil cooler as well, depending on the model purchased.
it has a bad head gaskit
System pressure will run abnormally high, the AC system will vibrate, and you won't get proper cooling.
Oil is used as the x-ray tubes cooling system.
Take it to an oil change place and have them do a cooling system flush immediately.