Huge odds. People were anti-vaxxers before, and were just looking for an excuse to justify their position. Goal post moving is a thing to be expected nowadays
See for example https://fivethirtyeight.com/features/unvaccinated-america-in...
There’s a pretty stable “never” population at 14%, and you see that as time goes on the hesitants have been gradually been getting won over.
I’m sure some in the “never” camp are using “it’s not been approved” as their current first-line given reason. But I think you need to break down the groups a bit more. There are genuinely people who are not fundamentally anti-vax that are just nervous about how fast the vaccines were developed or scared about what having “RNA” in the vaccine means (I don’t share these concerns but I understand where they come from). Some of these people will at the margin be persuaded by things like full approval.
Maybe some. But, while I don't really like governments and big employers wielding sticks in this case, you'll probably see even more people decide that they're not hesitant enough about vaccines to lose their jobs or be excluded from a lot of activities.
And while those sort of requirements could be implemented before full approval, a lot of organizations apparently wanted the additional air cover.
For 20 year-olds, kind of the opposite currently. Costs very little to use this choice as a political signaling gesture. But if the cost increases, as you say, behaviors will change and people will change their position. Talk is cheap, it’s easy to say “never” when it costs you ~nothing to do so.
But in short, I do strongly agree that mandates will be more persuasive than just approval alone. But I think full approval will still be beneficial in places that won’t make mandates.