As long as you've placed your baby on it's back while sleeping the baby should not choke on the vomit while sleeping.
The baby has natural ways of preventing the vomit from choking them so there's usually no need to worry as your baby can prevent the spit up or vomit from going down the windpipe and causing choking.
Make sure your baby is sleeping on it's back at least until they're older than 1 year to prevent SIDS as well.