Yes. There are virus vector vaccines already in existence: https://en.wikipedia.org/wiki/Viral_vector_vaccine

For example, adenovirus vector vaccines were created for COVID-19: https://en.wikipedia.org/wiki/COVID-19_vaccine#Adenovirus_vector_vaccines

Those are non-replicating though.

Live attenuated vaccines also exist – which can replicate – but those work by using a weakened/modified version of the original harmful live virus the vaccine is intended to protect against: https://en.wikipedia.org/wiki/Attenuated_vaccine

Oral polio vaccine is a well-known example.

That’s what you call a viral vector. Apparently the Sputnik V vaccine for COVID used this approach.

Edit: Sorry, wait, do you mean like designing a viral vector-based vaccine and spraying it into the air to vaccinate everyone around? That seems like it’d run afoul of some kind of ethics things.

Kind of. It’s called inoculation. The best example is if you caught cow pox you became immune, or nearly so at least to small pox which was deadly

There are oncolytic viral therapies, where viruses are modified to kill cancer cells. So, sure probably.

This a good thought, but I think that’s how you get the T virus.

Most early vaccines were less dangerous viruses related to more dangerous ones and which provided cross-immunity once free immune system had learned it.

Then there’s been plenty of vaccines with dead virus particles, as well as modified live viruses (dangerous viruses which was weakened, neutralized, or sterilized, or even mild viruses equipped with recognizable but harmless proteins from dangerous viruses) to more safely expose you directly to the pathogen.

Then mRNA and protein subunits and some other types drops the full virus part and provides methods to expose you to only small pieces

It’s generally speaking risky to try to create custom infectious viruses. A significant factor is that triggering the mechanisms for mass production of virus particles in the body can be enough to trigger harmful reactions (immune dysregulation, cell death, etc). Stuff like this is why even viruses you think are harmless still kills people every flu season

This was close to the plot of the 1973 science fiction story “By Any Other Name” by Spider Robinson, later expanded to the novel “Telempath”. The story won a Hugo award but the virus scheme didn’t work out so great.

https://www.projectrho.com/public_html/rocket/apocalypse.php#smelly2

Probably

Even if you were to create a novel virus to achieve that goal something nasty would eventually evolve to mimic it and we’d have no defense.

So you want to engineer a living, evolving, highly contagious virus that contains enough of a dangerous virus to train your immune system to be resistant to that dangerous disease?

Do you not see how bad an idea that is?