Yes, but it would depend on the results.
The problem is that most people are bad at risk assessment. If COVID-19 vaccine increased their risk of premature death by .0000001% they point to that and say sure not taking my risk! Despite the fact that they'd be at much more risk of dying by getting the disease, or just hopping in their car and driving down the street to get a loaf of bread of whatever.
If you showed say, a 1% uptick in mortality that you could attribute to the vaccine, yea that would be a different story. But guess what? We wouldn't* release such a vaccine.
* I add an asterisk here because if it was a 1% uptick in mortality you can think of scenarios like a disease which kills you 50% of the time or something around that range as being a worthwhile trade off for a 1% rate.