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.

The thing is people 'on the other side' think exactly the same, but come to different conclusions. For instance what do you think the chances of a healthy 20 year old male with 0 comorbidities of dying from COVID are? And what do you think his chances of suffering a significant case of myocarditis or pericarditis from the vaccine is? By "significant" I mean a case that's significant enough to result in active diagnosis - in other words somebody being diagnosed after a visit to an emergency room, as opposed to passive diagnosis where you assess each vaccinated individual to find cases that would otherwise go undetected.

Obviously I'm not comparing apples to apples (side effects from vaccine vs death from COVID) but this again is as explained by your own logic. If we were having a smallpox outbreak (with some strains having upward of 30% mortality rates across all demographics), I'm not going to be concerned about side effects of vaccines short of death. But with the rather low risk profile of people in favorable health/age demographics, the side effects of vaccination become quite relevant. Another issue is that early on it became quite apparent that the vaccines were not stopping people from getting COVID, so it's not like you can really compare vaccine vs covid effects, because the reality is you're probably still going to get COVID (and repeatedly, as it turned out) regardless of vaccination status.