It's really looking like laws vary by state.
Here's some great info:
https://www.dnr.sc.gov/news/2018/may/may8_turkeyeggspoults.html
South Carolina:
Here's some great info:
https://www.dnr.sc.gov/news/2018/may/may8_turkeyeggspoults.html
South Carolina:
However, state law is clear on this subject and provides that it is unlawful to rob any wild turkey nest or to possess wild turkey eggs.
Laws prohibiting robbing turkey nests and possessing eggs are in place for a good reason. Wild turkeys that are hatched by humans lose virtually all of the instincts that allow them to survive in the wild. Additionally, many attempts to hatch eggs are for the purpose of raising the birds to be released in an effort to increase local turkey populations. However, not only do these pen-raised turkeys have poor survival, they are often comingled with other domestic fowl which may harbor diseases that could be detrimental to wild turkeys in the area if the pen-raised birds escape or are released. State law also prohibits the release of pen-raised turkeys into the wild.