The headstone has no bearing on when a deceased is buried. In some cases, a person has pre-purchased their headstone or grave marker and it may already be installed on the grave at the time of burial. In most cases, however, the marker is not even purchased until death has occurred. Once purchased, the time frame to make and deliver the marker is about 6 weeks to 3 months, depending on the type of marker purchased.
There is no circumstance where the burial of a deceased (no matter what the cause of death) would be held up for a headstone to be made/installed. Since decomposition begins at death, embalming and/or refrigeration services would be used if there was a reason the deceased could not be buried within a few days.