Most likely NO.Shipping companies only ship
You can always pack the container yourself and ship House/House (FCL or LCL), but that wasn't the point. I was talking about international MOVING companies, and they do take care of everything. They pick up your stuff, put it in a container at their storage facility, ship it to the port of destination and arrange for transport to your new home at the final destination, where the container is unpacked again. I've done that multiple times across continents. No prob whatsoever.
Try to handle the shipping yourself though, and you are setting yourself up for failure. There's a reason why there are shipping agents and specialized moving companies.