You'd think so but it's actually the other way around: the people most likely to die are not given vaccines (because there's no point). This can be seen in the UK data where increasing vaccinations causes an increase in deaths in unvaccinated people from non-COVID causes. Clearly that's not a biological link - rather, what's happening is that as the vaccinated population grows, the really sick and dying people get concentrated in the unvaccinated cohort, which then experiences higher death rates.
Data is tricky, especially with something like this.
This effect may exist, but it's dominated by the wider UK population in which vaccination rates for over 80s are 95% and vaccination rates for under 40s closer to 60%, and care homes and immunosuppressed people were priority targets for vaccination. There are people who are considered too sick to be vaccinated, but I don't think they feature significantly in COVID ICU admissions, not least because ICU isn't likely to save them for the same reason they weren't vaccinated
The UK data also shows that all age groups are proportionately far more likely to be admitted to an ICU bed if unvaccinated. I don't think the majority of under 40 ICU COVID admissions who were unvaccinated were unvaccinated because they were already expected to die soon.
This effect may exist, but it's dominated by the wider UK population in which vaccination rates for over 80s are 95% and vaccination rates for under 40s closer to 60%, and care homes and immunosuppressed people were priority targets for vaccination. There are people who are too sick to be vaccinated, but they don't tend to make it to ICU beds for COVID.
The UK data also shows that all age groups are proportionately far more likely to be admitted to an ICU bed if unvaccinated. I don't think the majority of under 40s admitted to ICUs who were unvaccinated were unvaccinated because they were already expected to die soon.
Data is tricky, especially with something like this.