Capillary action will slowly perfuse the wood. That depends on molecular size, temperature and time.
It doesn't replace the wood air. Soak for days = will that last, stirring stew. No.
Charles Law predicts that heating that wood will expand that wood air and push out the oil finish
to be replaced by whatever the hot liquid was at that time (soup?).
This is why old wooden spoons look black like the bottom of a compost bin = that is what they have become.
This seems to me to be the major reason for a really penetrating oil finish.
I'm done forever in 3 minutes and 30 seconds.
Oxidation? Possible. As a % of the wood surface area, very little oil can be exposed to the air.
I ignore it. Use the oil finish of your choice. Pharmaceutical-grade mineral oil doesn't oxidize.
I buy Iliada Kalamata Greek olive oil in 3-liter tins. Has been working for me for years now.
I carved a kitchen slop-dish in birch to hold wet sponges, sink stoppers, scrub pads, etc.
I painted it with bees wax. Knowing that waxes all melt at about 150F or so, into the 325F oven.
That dish is now permanently waterproof.
It took me a week to clean all the wax spatters off my stove top = ultra messy.