I believe you are thinking right. Once you get your sink out, you will probably have to beat the top off because it is most likely glued down. Your procedure plan is exactly what I would try.
Is the backsplash made into the top? If it is a separate piece, recommend you take it off first if possible. Either way, you will likely have a bit of damage to the drywall. If it's insignificant damage, the new backslash will cover it.
You can also patch any bigger areas with drywall patches and some joint compound.
Remember safety. Since it is marble, it could splinter, so don't forget the safety glasses, long sleeves and work gloves.
Is the backsplash made into the top? If it is a separate piece, recommend you take it off first if possible. Either way, you will likely have a bit of damage to the drywall. If it's insignificant damage, the new backslash will cover it.
You can also patch any bigger areas with drywall patches and some joint compound.
Remember safety. Since it is marble, it could splinter, so don't forget the safety glasses, long sleeves and work gloves.