If you drink it now, would you stop?

Almost no-one can honestly answer this for themselves. I think the truth is likely: 'no, I'd still order a coke at McDonald's, I'd still pick a coke up from a vending machine if I'm thirsty. But if I'm buying a takeaway sandwich, I might not also get the drink. Or if I'm in the supermarket, I might just skip that aisle.'

I'm sure it's almost completely subconscious.

Yes, but not because advertising lets people know about Coke. The people who still know about Coke would be the same after a year, I imagine.

The mechanism of how advertising works seems to be not that. I think repeatedly brand exposure does something to the brain and decision making that we don’t fully understand.

Familiarity, I think.

Exposure breeds familiarity, which breeds desire, I think.

Even if all you hear is an occasional ad about the company, you might get curious and research them yourself.