Not quite. As the coolant heats it expands and is less compressible than the gas (air). The pressure rises but the ar is compressed from o psig to say 15 psig i.e .1 atmosphere above atmospheric pressure.

If the vent cap on the expansion tank is below the fluid level in the rad then fluid will auto syphon out of the expansion tank if the vent cap opens assuming the rad is full of coolant of course.

Expansion tanks normally have marks to show a fluid level & then a head space.
You can see on Belle that the fluid level in the expansion tank is level with the top of the rad & then there is an air gap. I marked the line with tape because MMC reuse header tanks, in this case a Ford Fiesta and the marks on the tank are not relevant.

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JohnV6
2022 CX Plus Four
2025 MG ZS EV aka Trigger