Vaccination has NOTHING to do with GMO.
Keep studying.
Also, very few things pass from hen to chick - Salmonella is the most obvious, because the bacteria that causes it lodges in the birds ovaries. Also, Mycoplasma, and some really rare stuff.
There is no Salmonella vaccine. There is one for MG in chickens, though in commercial focks, they simply destroy the infected birds and start over. A practice I am prepared to follow myself (as an NPIP participant, my birds are tested annually, and I've agreed in advance to do so in the case of an infected flock).